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COPYRIGHT DEPOSIT 



NOTES ON 

Technical Sketching and Free Hand Lettering 

' FOR ENGINEERING STUDENTS . 



ALTON L.'-'^'iITH; M. S. 
Professor of Machine Design 
Worcester Polytechnic Institute 



PUBLISHED BY THE AUTHOR 

WORCESTER, MASS. 

1909 



Copyright, 1909 

By Alton L. Smith, M. S. 

Worcester, Mass. 






2 47«8'4' 
r.i. * 

SEP 23 1909 



IV 



PREFACE 

The modem engineer must know how to make drawings in order to know how to read them. However, 
verj- Uttle of his time is spent at the drafting board. His dra-^xnngs consist mainly of sketches showing his ideas 
in more or less detail and which are turned over to subordinates to be worked out and put in the conventional 
form. In the solution of his construction problems, he is obliged to keep in mind all thi-ee dimensions of materials 
and a preliminar}- sketch stands in the place of a model which he can work over and examine in order to clarify 
and fix his ideas. Such sketches must often be made in great profusion and dexterit}- with the pencil is fre- 
quently an inspiration to the brain. 

One of the primaiy functions of a course in drawing is to cultivate and extend the faculty of "thinking 
in space.'" In acquiring this faculty, the draftsman must be able to express his ideas quickly and accurately 
through the medium of drawings. He must also learn to read correctly the ideas of other engineers as expressed 
in drawings. 

The actual construction of an object from the drawing representing it is a ci-ucial test of ability to read 
that drawing. There are many disadvantages of such a test applied for that purpose alone and it is believed 
that the translation from a projection drawing of the object to an axometric or isometric representation meets 
aU the requirements of the case with far less expenditure of time. The reverse process also gives a most valuable 
training and the author believes, after long experience in this work, that the methods herein presented secure 
the best results with the least effort. 

Though devoted primarily to the teaching of drawing, the illustrations and problems have been selected 
so as to give the student familiarity with a wide range of modern manufacturing and engineering practice. A 
considerable amoimt of material has been added for this second edition and the author wishes to thank the 
many friends who have provided material or given suggestions. The author wishes to thank Prof. A. W. French 
especiaUj^ for assistance with the chapter on Structural Drawing. 

Worcester, Aug. 3, 1909. Alton L. Smith. 



CONTENTS 

Chapter I. , page 
Description of Methods of Representation 7 

Chapter II. 
Shop Drawings and Blue Printing 16 

Chapter III. 
Miscellaneous Details of Construction 34 

Chapter IV. 
Toothed Gearing 45 

Chapter V. 
Structural Drawing 56 

Chapter VI. 
General Suggestions on Technical Sketching 67 

Chapter VII. 
Sketches for Shop Drawings and Electrical Symbols 74 

Chapter VIII. 
Geometric Perspective and Artists' Perspective 81 



Chapter IX. 
Axometric Sketching ^' 

Chapter X. 
Isometric Drawings and Cabinet Projections 98 

Chapter XI. 
Comparison of Methods of Representation 101 

Chapter XII. 
Shade Lines and Line Shading 103 

Chapter XIII. 
Free-Hand Lettering 108 



Tables 125 

Index 133 



LIST OF TABLES. 

Table 1. — Decimal Equivalents of Common Fractions. Whitney or Woodruff Keys. 

U. S. Standard Bolts and Nuts 125 

Table 2. — Machine Screws, A. S. M. E. Standard. Machine and Wood Screw Gage. 

Twist Drill and Steel Wire Gage 126 

Table 3. — Properties of Wrought Iron Pipe 127 

Table 4. — Standard Tapers. Brown & Sharpe and Morse Standards 128 

Table 5. — Gage Lines. Rivet Spacing. Rivet Dimensions. Clearances 129 

Table 6. — Dimensions of Ball Machine Handles. Standard Washers . . . ^ T .... 130 

Table 7. — Dimensions of Flange Couplings ^'^ ... * 131 

Table 8.— Weight of Materials . yc^. 132 



CHAPTER I 

DESCRIPTION OF METHODS OF REPRESENTATION 

1 . Probably the best way to describe a material thing is to make a picture of it, and a written language 
composed of hieroglyphs would prove satisfactory if it had to express only what we sense through the eyes. 
To depict odours, soimds or emotions would severely tax such a language as reference to the ancient Egyptian 
monuments will prove. 

The written language of modern engineering construction has to deal chiefly with shape and size of material 
things. It is a picture language and its superiority over the language in coramon use will be quickly recognized, 
if one attempts to read a written description of a modern machine without the aid of an illustrative drawing. 

A perusal of legal documents wiU show how difficult it is to express an idea or fact concisely and with 
exactness. In the modern sciences, extended terminologies permit this. There is, of course, a special vocab- 
ulary of technical terms used by engineers and shop workmen, and it would be possible to write a specification 
describing each part of a machine so it could be built, but to write and to read such a description would be a 
tedious and a costly process involving many chances for error. There was a time when construction was carried 
on in shops by oral directions from the foreman, or the workman made a part of a machine to suit his own notions, 
very much as some repair work is now done. If such methods had prevailed, the general use of our numerous 
modern contrivances would have been deferred to the remote future. 

2. An engineering drawing must describe the machine or structm'e completely, exactly and concisely 
that it may insure economy of time for the maker and the reader. Most drawings used in engineering work 
are made mechanically with instruments, because most of them can be thus made more economically. There 
are, however, many drawings which an engineer or draftsman has to make, where it would be very impracticable 
to make them with instruments. Such are the innumerable preliminary sketches used in designing, the inciden- 
tal sketches made for illustrative or explanatory purposes, sketches of parts of existing machines and sketches 



for work of which no record is preserved such as repair jobs. It is also true that some desirable forms of repre- 
sentation which can be made well and quickly free-hand, become expensive when drawn with instruments. 

3. The problem in illustrative drawing is to produce a representation of an object having three dimensions 
on a flat surface having only two dimensions. The difficulty lies in properly representing the third dimension. 
The different methods for accomplishing this, their underlying principles and their adaptation for mechanical 
and free-hand treatment will be considered. 

Nearly all simple objects can be represented without ambiguity by a single outline drawing. A stick of wood 
looked at endwise tells nothing regarding its length. It might be a block or a long beam. By looking at it from 
some other point of view its true proportions are indicated. In the case of a sphere the outline from any poiat of 
view is a circle. There are three ways of completing this representation. If we draw a circle and write "sphere" on 
it, the size and shape are defined. If we draw two circles and indicate that these are views from two different points, 
the object is defined. If we draw a circle and shade its surface to represent the light and shade effect on the original, 
the object is defined. Each method has its advantages dependent on the use to which the drawing is put. 

4. If a die is held close to the face, but far enough from the eyes to be seen distinctly, it wiU appear 
as in Fig. i, A. On closing the right eye it appears as at B and on closing the left eye, as at C. The fact is, 

we get a separate image of the object with each eye and if both eyes are open the 
two images are merged more or less into one. To test this, set up a card about 10 
inches high edgewise between B and C and look at the figures from the top edge, 
the card serving as a partition to shield B from the right eye and C from the left. 
These two images will always occur when both eyes are used, but the difference 
between the two is not noticeable, except when the distance of the object from the 
eye is small as compared with the greatest horizontal dimension of the object. A drawing like A would not 
be a satisfactory representation of the die, but either B or C would be satisfactory. We therefore derive the 
conclusion that to make a satisfactory representation of an object, it should be drawn as seen with one eye. 
It is also true that if this drawing is to produce the same effect on the eye that the original object did, it 
should be looked at with one eye, the drawing being held at the same distance from the eye as when made. 



B 



I I 



Fig. 1. 



Stereoscopic photographs made in pairs and viewed in the stereoscope give an increased reality to the third 
dimension. A similar effect is produced when a single picture is viewed with one eye through a conical tube, 



or through the closed hand. 




Actual D/^Aw/Nei 
ON Picture Plane 



Fig. 2. 

5. Referring to Fig. 2, A, we have a cube ABCD-H resting on the right end of the top of a table OPQ. 
Let the eye be placed at E and interpose a transparent piece of glass KLMN between it and the cube. The 



10 



cube is visible to the eye, because light is reflected from its faces and as these faces have different degrees of 
illumination, their bounding edges appear conspicuously as lines. We may consider that the light reflected 
from any point, B, on the cube to the eye passes along a straight line, BE, through the glass at some point b. 
If we mark this point, b, on the glass, it will shut off our view of the corner, B, of the cube which is in line with 
it. In the same way, we may mark the other points on the glass where we see the other corners of the cube. 
These points are now connected forming lines which appear to coincide with the edges of the cube. That is, 
line ab shuts off edge, AB, be shuts off BC and in the same way, the others. The cube could now be removed 
and the figure abcd-h would produce the same effect on the eye that the edges of the cube did. It stands in 
place of, or represents the cube. Such a drawing is called a Linear Perspective. It is designated Linear because 
it represents lines, but not the light and shade nor the color effect. 

Fig. 2, B, is the actual drawing, as it is on the glass plane. The 
transparent plane is called the picture plane. The line ES from the eye 
to the center of the object is called the line of sight. 

6. If in Fig. 2, A, the picture plane is revolved about the line X-Y as an 
axis, until it is perpendicular to the line ES, the perspective drawing would 
change to that shown in Fig. 3, A. Here the upright edges are not quite ver- 
tical and produce a false impression regarding the object. If they are made 
vertical, as in Fig. 3, B, the drawing will be an Artists' Perspective of the cube. 

7. Referring again to Fig. 2, A, suppose the eye to be moved along the line SE so that it is much further 
away from the object. Then the angles which the light rays make with each other at E would become much 
less. If E were removed along SE to a very great distance, then the angle between the light rays would reduce 
practically to zero and the light rays would become practically parallel. The drawing on the picture plane 
would be called an Oblique Projection. It is so called, because if we projected, or threw on the picture plane, 
each point of the object by a series of parallel lines oblique to the picture plane, we should get the same result. 

8. If the cube in Fig. 2, A, were placed further to the left with its front face parallel to the picture plane 
the perspective drawing of it would be like Fig. 4, A. If an oblique projection were now made by removing 




ARTIST'S' 

Peirspective 




Fig. 3. 



11 



the eye to a great distance, the drawing would be like Fig. 4, B. Such a drawing is called a Cabinet Projection. 

Its peculiar features are that one face of the object is shown in its true size 
and shape, while lines perpendicular to this face appear inclined at 45° 
and of one-half their true length. 




Fig. 4. 



fl- b 


Sf 


OffTHOQffAPHIC 

Projection 




d C 


h 



Fig. 5. 



9. Referring again to Fig. 2, A, suppose the eye be removed to a 
great distance from the object along a line RE which is perpendicular to 
the picture plane. The light rays from the object 
to E would then become practically parallel to RE 
and therefore perpendicular to the picture plane. 
The drawing on the picture plane would then become like Fig. 5 and it would be called 
an Orthographic Projection, because if the object were projected on the picture plane by 
lines perpendicular to that plane, we should get the same result. The term projection 
is always understood to mean orthographic projection unless otherwise stated. It is 
thus apparent that a projection drawing is merely a perspective drawing in which the 
eye is placed at a great distance from the object. 

10. In Fig. 6, A, the cube, ABCD-H, is elevated sHghtly from the table and turned so all its edges are 
oblique to the plane of projection. It is also placed so its upright edges are all parallel to a side plane, not shown, 
but which is perpendicular to the table top and the plane of projection. If a projection of the cube is now made 
on the vertical plane, its actual shape will be like Fig. 6, B. If this drawing be compared with Fig. 2, B, a 
marked similarity is noticed, although there are also important differences. A projection made in this way 
is the basis of an Axometric Drawing. 

11. If the cube in Fig. 6, A, had been placed so that the three edges meeting at a corner, as for instance 
B, were equally inclined to the plane of projection, then the resulting drawing would have been like Fig. 6, C. 
This is called an Isometric Projection. Its peculiar features are that the three edges meeting at B are 120° 
apart and equal in length. Any line of the drawing, as for instance, be, is shorter than the edge of the cube 
it represents. 



12 

12. If a drawing were made of the cube, which was exactly like Fig. 6, C, in shape, but in which the 
lines be, ab, bg etc., were each equal to the true length of the edge of the cube then we should have an Isometric 
Drawing. An isometric drawing is exactly like an isometric projection, but larger. 

ISOf^E.TRIC PflOJECT/OH 




Fig. 6. 



jHCTu/iL Project. 
OF THE Cube 




13. Solids have three principal dimensions; length, breadth or width and thickness or height. These 
terms are applied in various ways, depending on whether the object is large or small, movable or fixed and other 



13 

characteristics. The essential thing to remember is that these three dimensions are perpendicular, each to the 
others. It might be difficult to agree on the length, breadth and thickness of so irregular a form as a potato, 
but three measurements could be arbitrarily assumed, which would have the essential feature of such dimensions, 
namely, mutual perpendicularity. In the case of most artificial forms, however, there is little difficulty in select- 
ing these principal dimension lines or reference axes of measurement. Generally they wiU be partly or entirely 
determined by the physical peculiarities of the object. The rectangular block and the circular cylinder are 
the predominant artificial forms. In the former, the edges, and in the latter the axis of sATnmetr}' and two per- 
pendicular diameters would be selected. In the case of the sphere, three perpendicular diameters would be chosen. 

If a drawing is to be useful as a guide in construction, it must satisfy the following conditions : 
First, it must give an idea pictorially of the shape of the object. 

Second, it must be of such a nature that aU necessar}- dimensions and specifications can be appended. 
Third, when completed with all dimensions and specifications, the whole must be capable of being read with 
a minimum amount of study. 

14. To permit satisfactory- application of dimensions, the object must be placed so its projections show 
the lines of the object in their true length. To accomplish this, the object must be placed so two of its principal 
dimensions are parallel to the plane of projection. The result of this is to lose the third dimension, so that 
nearly always two or more projections of the object are required. 

In Fig. 7, the object to be represented is a triangular pyramid JKL-0. It is placed inside a glass box 
ABCDEFGH, the back side of which is lacking. A working drawing for such an object should give the size 
and exact shape of the base, the length of the altitude and the location of the vertex relative to the base. The 
pyramid is therefore placed with its base parallel to the top face of the box and this location brings the altitude 
parallel to the front face of the box. One side of the base, JK, is parallel to the face BCFG. The pyramid 
is now projected onto each of the five faces. The joints of the box along edges AE, BF, CG and DH are then 
broken. Keeping the front face, ABCD, stationary, swing the top, bottom and two side faces about their hinge 
lines AB, CD, BC and AD, imtil they come into the same plane with the front face, as shown. 



Third Angle 
Projection.^ 




Fig. 7. 



15 

15- The projection figures on the four revolved faces are now grouped about the central projection on 
the front face and certain features of their relations should be noted. 

Considering the central projection, or front view, the principal one, it is seen that the view obtained 
from above the object, that is the top view, is placed above the front view; the view of the right side is placed 
at the right ; the bottom view below and the left view at the left of the front view. This is a logical arrange- 
ment and it is called third angle arrangement, or Third Angle Projection. 

This is the arrangement of views used in nine-tenths of the drafting rooms in the United States. The 
other arrangement most used is known as first angle projection. With this method of grouping, the top view 
is placed below the front view, the bottom view above, the right view at the left and the left view at the right. 
It is entirely illogical, renders a drawing more difficult to construct and to read and has advantages in only a 
few instances. First angle projection is used for shop drawings in Great Britain, on the continent and by the 
other tenth of draftsmen in the United States. 

i6. It should be noted next, that any point of the object, as the vertex 0, will have its projections in 
the front, left and right views, that is 0^, 0* and 0^ on the same horizontal line. Also any point, as 0, will 
have its projections in the front, top and bottom views, that is, 0^, 0^ and 0^ on the same vertical line. This 
relation between the views is a very important one, and it facilitates greatly the making and reading of the pro- 
jections. 

17. Inspection of the projections shows that two views, the front and top would suffice in this case to 
represent the object, and accommodate all necessary dimensions. Thus the top view shows the exact size and 
shape of the base and the location of the vertex, while the front view gives the exact altitude. Though two 
views are really necessaiy here, for some objects, one view would suffice. On the other hand, for some very 
irregular machine parts, five views supplemented by auxiliaiy sections, dotted lines and specifications are none 
too many, to make them intelligible. 



16 

i8. The names used in Fig. 7 for the different projections are those commonly emploj^ed. Others are 
also in use for architectural drawings and Descriptive Geometry. They are given in the following table. 

Common Name Architectural Drawings Descriptive Geometry 

Front View Front Elevation Vertical Projection 

Top View Plan Horizontal Projection 

Right View Right Elevation Right Profile Projection 

Left View Left Elevation Left Profile Projection 

Bottom View Plan Aux. Horizontal Projection 

CHAPTER II 

SHOP DRAWINGS AND BLUE PRINTING 

19. A working drawing is one used by a workman in actually making the machine or structure which 
it represents. 

20. While many of the methods of representation described in the preceding chapter might be used 
for working drawings, the one last described is usually employed. Though somewhat deficient pictorially it 
has the following advantages. The process of making the projections is easily explained and generally under- 
stood. The drawings are composed principally of horizontal and vertical straight lines and circles, all of which 
are easily made with ordinary instruments. The large number of views available makes it possible to avoid 
the confusion of lines and figures which occurs when one view only is used. 

21. There are two kinds of working drawings. A detail drawing shows each piece by itself with complete 
dimensions and specifications for its construction as shown in Fig. 9. An assembly drawing shows all the parts 
of a machine or structure assembled, or put together: Or it may show a group only of parts put together. A 
drawing of an engine would illustrate the first, while a drawing of the connecting rod of an engine would illus- 
trate the second. An assembly drawing may be used in a pictorial way, merely, to give a general idea of the 



17 

machine, in which case, much of hidden detail is not indicated and only the principal dimensions are given- 
Such a drawing may be used for assembling or for erecting the machine and then everything is shown in 
greater or less detail, but with only a few dimensions. An assembly drawing may be used as a shop drawing 
for actual construction, and then complete dimensions are given for every detail. It is obvious that only the 
simplest machines, tools or structures could be thus drawn. A shaft hanger or a monkey wrench would be 
illustrations. Such a drawing has an advantage over a detail drawing, in that there is less chance of error, 
both in making the drawing and in making the parts. In the case of the draftsman, the drawing helps to 
check the dimensions and in the case of the workman, he sees how the parts fit together. If a machine is 
made on the interchangeable system, this last feature is of no particular value. 

22. Scale. Drawings should be made large enough so they can be easily and accurately read when 
covered with dimensions. For convenience in filing, most drafting departments have adopted standard sheet 
sizes, which are particularly adapted to their special line of work. 

It is often desirable to place on one sheet all the parts of a machine constituting a natural group ; for 
instance, all the parts of the tailstock of a lathe; or all the forgings; or all the castings. These conditions, there- 
fore, will usually determine the scale. A bridge is drawn to a greatly reduced scale, the general run of machine 
parts are drawn full size, while instruments or machines with exceedingly small parts, like those of a watch, should 
be drawn larger than full size. 

23. The scales in common use are as follows, 12 inches, 6 inches, 3 inches, 1^ inches to one foot for ordinary 
details of machinery ; 1 inch, | inch, J inch, | inch, I inch and | inch to one foot for larger structural work. A 
drawing made to a scale of 1^^ inches to one foot is one in which 1| inches on the drawing represents one foot in 
the object; that is, the drawing is ^ of full size. Full size is a very desirable scale, especially for the designer 
when sketching small details because it conveys an exact idea of the size of the part and there is also less liability 
of errors in dimensioning. 

Some drafting rooms are provided with large vertical boards ruled with squares and used for full sized 
layouts. Such a layout is particularly useful in designing a new machine. 



18 

SELECTION OF VIEWS 

24. Select those views and the least number of views that will completely and clearly represent the 
object. Do not use two views, if one will suffice. If more than one view is necessary, one of them should be 
the front view, as this makes it possible to project from points in one to corresponding points in the other projection 
by horizontal or vertical projecting lines. In Fig. 7 the object might have been placed so as to make a front view of 
what is now the right view. A corresponding change in the positions of the other views v/ould have been necessary. 

A judicious use of dotted lines or of sections will often permit a reduction in the number of views, as 
is explained in Sections 29 and 30. The pipe fittings in Fig. 11, the Latch Handle in Fig. 8, A, and the Spur 
Gear in Fig. 16 illustrate this. On the Lag Screw in Fig. 10, by specifying Sq. Head, an additional view is 
avoided. Also in the Anchor Bolt for concrete in Fig. 10, by giving the letter d after the |" dimension, a round 
bar is indicated thus making one view sufficient. 

25. While limitations of space or the clearness of the drawing may sometimes decide otherwise, yet 
the desirable and the customary front view is that view which shows the object most characteristically and in 
a natural position. For a building, it would be the facade; for a bridge, the longitudinal view; for a pulley, 
the view showing the radiating arms; for a machine, the view a workman gets as he stands at work before it. 
Some objects have no characteristic view, others have several and a moving part like the crank on an engine 
may have many natural positions. These are exceptional. 

26. It is allowable to have one view showing the object with a part removed as in the Cylinder Cap, 
Fig. 9, while another view may show it entire or with a different part removed as in the Worm Gearing, Fig. 
16. To condense a drawing, it is often desirable to break out a portion as in the Pulley, Fig. 9. Under Broken 
Ends in Fig . 8 is indicated how to break rods, pipes, structural steel etc ., so as to suggest the shape of the cross-section . 

An auxiliary view is sometimes needed which cannot properly be grouped with the other views. Its 
location or relation to the others must be very definitely specified by projecting lines or otherwise. 

27. When two pieces are exactly alike except in some minor detail or dimension, it is often possible to 
make one drawing serve for both, as in the Hoist Arm Yoke, Fig. 9. 



19 

28. Threaded Parts are so numerous that to save the draftsman's time they have been conventional- 
ized. The same is true regarding Riveting in Structural Work, and the Fittings in Pipe Systems. These are 
represented in Fig. lo and Fig. ii. 

USE OF DOTTED LINES 

29. Some draftsmen show all hidden edges, but this is plainly a mistake, for in many instances it produces 
only a confusion of lines and obscures the meaning of the drawing. Hidden edges should be shown, only when 
they contribute to the clearness of the drawing or give it a more finished appearance. Thus in Bevel Gears, 
Fig. 16, the dotted lines complete the representation partly shown by the half section. See also Section 81 for 
the proper way of making a dotted line. Figures 9, 10, 11 and 16 illustrate the use of dotted lines. 

USE OF SECTIONS 

30. A slice or section is used to show the contour of an irregular shape or of a shape not clearty showm 
by dotted lines. The section of the pulley arm. Fig. 9, and of the Latch Handle, Fig. 8, A, are illustrations. 
The section may be specified in any one of the three ways shown in Fig. 8, A. A section of this kind shows 
nothing more than the figure cut from the object by the sectioning plane. 

31. A sectional view is one which shows not only the cut surfaces, but everjiihing back of them also. 
The chief use of a sectional view is to explain the internal construction of the object. In Fig. 8, B, is an illus- 
tration of this. Note that the center is not cut, as there is nothing inside of it to be explained. Sectioning planes 
may be taken in any way to facilitate the explanation of the object, but they are usually taken parallel to some 
one of the planes of projection. Unless the location of the cutting plane is perfectly obvious, it should be indi- 
cated by its projection on the plane to which it is perpendicular, where it will be shown as a line, marked as 
in Fig. 8, A. 

A common exception to the rules of sectioning is shown in the Pulley, Fig. 9. 

32. Sometimes when it is not desirable to remove the part of the object in front of the sectioning plane j 
a dotted section may be used as in Fig. 11, V. 



Cast ihon 



.H^f/^p^— gj^g^, Use of Sections 



BROKEN Ends. 





Q Max. Space: Width 



OF AREA. 



BRicn 



^^ 



z/M /: /:/:X<^ ^ ^ A 



v/////y/////m 



A Sectional \//ei/\/ 

C/foss Lif^iN^ or o//nr£^euT f^/trs 
oFrHE Same Piece /s the Same. 



Rubble 



CoNCfiEre 







:0 '"^ 0"* '_? ' 



O • >« 'fl 



,o;0. 



«;<i 







5/^A/^ 


Eaf^th 


iiSfS 


wmiim 



WATEF( 




SeCT/oa/ Lining /vic/jt /vot- 



Fig. 8. 



21 

33- Section lining or cross hatching may be at any angle, so long as it is not parallel to the bounding 
lines of the surfaces sectioned. The angles generally used are 30°, 45° and 60°, which taken both ways give 
six directions. If two different pieces come together in the same section, as in Fig. 8, B, a different angle should 
be used for each piece; but for different parts of the same piece, even though disconnected, the same sectioning 
will be used. Width of spacing is determined by the smallest sectioned part of a given piece and large areas 
may have wider spacing than small ones. Fig. 8, C, shows satisfactoiy spacing for different areas. 

34. The kinds of material used in construction have multiplied to such an extent in recent years, that 
it is no longer feasible to have a distinctive symbolical section lining for each. In Fig. 8 are showTi some of the 
kinds which are in use chiefiy in a pictorial way. On a working drawing these are seldom used, plain section- 
ing and definite printed specification of the material being the custom. 

35. Section lining is one of the most tedious parts of a draftsman's work. To secure uniform spacing 
on large areas, a special instrument is often used. For ordinary work, spacing by the eye is sufficiently accurate. 
Make the first few spaces carefully and then look back to them frequently for a gage on the other spaces, rather 
than at the last spaces made. For free-hand sectioning, the slant from the upper right to the lower left is the 
one to be prefen-ed for a right handed draftsman. 

USE OF CENTER LINES 

36. As has been pointed out in Section 13, nearly aU artificial forms have some line or fines with regard 
to which they are symmetrical. AU turned forms have an axis of revolution, links such as the Rocker Arm, 
Fig. 30, have an axis line connecting centers of holes. In a steam-engine, there is the axis of the cylinder, the 
axis of the crank shaft, the axis of the connecting rod and various others. Eveiy drilled or bored hole, every 
screw, bolt, gear and pulley has an axis. In making a drawing these lines are invariably dra^^^a first, because 
they are very useful in making measurements. They are called center lines in the drawing and are usually 
shown as dash and dot lines. They are base lines for measurements which the workman also must use in laying 
out his work. In the Bevel Geare, Fig. 16, they are used to indicate symmetr\', for dimensioning the angles 
and for distance between shafts. In the Pulley, Fig. 9, thej' indicate symmetry only, and this is their general 



I5'x4~ Pulley ... 

6ne-C.i7 Pat. NO./S3Z M' 



Sp/ral Gear Shaft 

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Pax A/o. 79 


A6 


B//^D£^ H/)/^OL E 


/ 


c./. 


P/iTA/o. 7S2 


A7 


B^tvi. fvficv: SHOe 


2 


Bff. 


PyfT.A/o.-^S 


AS 


Ho/srAfKM Yo/<£ 


2 


At.ST 


POR^.30or£i(g^- 



Fig. 9. 



23 

use for isolated shafts, bolts, screws, etc. While they are useful in making the drawings in this last case, they 
serve no purpose for dimensioning and for this reason are often omitted in such drawings where they would 
seriously interfere with dimension figures or specifications. Note the screws in Fig. lo. 

A center line is used for the pitch line of gears as in Fig. i6, and for bolt circles as in the Cylinder Cap, 
Fig. 9. 

DIMENSIONS AND SPECIFICATIONS 

37. It has been suggested that the projections in a drawing are important only as a suitable framework 
to which dimensions may be attached. This is an extreme view, as any draftsman who neglected his projec- 
tions would quickly discover. Projections are secondary to dimensions just as the whole drawing is secondaiy 
to the thing it represents and just as the machine it represents is secondan,^ to its product, and so on indefinitely. 
It is true however, that small errors in projections are frequent and sometimes permissible, though never desirable, 
while an error in a dimension maj- be fatal. The projection is used for illustration, while the dimension is used 
for measurement in construction. On this account, the dimensions and specifications of a drawing are its most 
important part. 

38. Three questions arise. What dimensions should be put on a drawing? Where shall they be placed? 
How are they expressed? Unless the draftsman has had actual experience with shop methods of construction, 
he will not be very successful in his selection of proper dimensions. His first inclination is to put on such dimen- 
sions as would enable the drawing to be duplicated. He must rather keep in nflnd the thing to be made, the 
tools the workman will use in laying out and measuring his work and the various machine operations to be per- 
formed. Constant study of approved shop drawings wiU give considerable information, conferences with the 
workmen will also be enlightening, but actual working on the machine in the shop is the best training for this 
part of the draftsman's work. 

The principal tools used by the shop workman are the two foot rale, steel scale, calipers, dividers, square, 
trammel points, straight edge, protractor, surface gage and other gages for threads, drills, wire, etc. 

The principal machine operations are turning, boring, driUing, miUing, planing, and grinding. Hand 
work such as filing, chipping and scraping should not be overlooked. 



24 

Besides the workman's tools and machines there are other considerations. For instance, many years 
ago, the shop workman was a man of extended mechanical experience, while to-day he is more or less of a machine ; 
oftentimes against his will. Instead of having an intimate knowledge of the machine he is helping to build, 
his knowledge often extends only to a part which he regularly makes. A drawing must therefore be made minute- 
ly specific and little should be left to the discretion of the workman. To this end, it is advocated that the dimen- 
sions which he will use directly should be put on the drawing, so that he need expend no inteUigence in adding 
up partial dimensions. Thus in the Spiral Gear Shaft of Fig. 9, the workman in turning from the f " end to 
the If" shoulder would like a dimension equal to the sum of -§4") liV" ^^'^ ^irw"- Such a dimension is seldom 
given by the draftsman, because he is interested only in the direct measurements which must be correct to per- 
mit fitting the piece to the parts it adjoins in the machine. If such a dimension is given, it should be in addi- 
tion to those which are direct. 

If there are finished flat surfaces on the piece, dimensions should be based on these and the same is some- 
times true regarding curved surfaces. Thus in the Pulley, Fig. 9, the thickness of the rim is based on a finished 
curved surface, but the thickness of the hub is not given by a measurement from the "bore." 

Location of parts of a piece are often made by reference to a center line, but care should be taken to 
see that this is a satisfactory way of locating. Such a method may be desirable oftentimes for the pattern- 
maker, but might be entirely inadequate for the machinist. 

It is impossible to lay down an invariable rule for the selection of dimensions, but the following is a good 
general guide. Put on those dimensions which will be common to fitted parts and which must be exactly right; 
also as far as possible, give those dimensions which the workmen will use in setting his tools to make the pattern 
or to machine the surfaces. 

39. The parts which go into machines and structures may be divided roughly into the following classes: 
Machine and hand forgings, castings, parts made in the screw machine from rod or bar stock and those numer- 
ous parts which are standard or semi-standard in form, such as bolts, keys, wire, pipe, sheet metal etc. 

Fig. 9, A 8, shows a simple forging with no machining called for except in drilling holes. If any of the 
surfaces were to be milled or planed it would be indicated by an / mark, so the blacksmith could make the part 



25 

thicker than called for by the dimension. In machining, the part would be thinned to the stated dimensions. 
Dimensions are selected as follows. For size of bar stock, f" thick and 2" wide. As all the fitting depends 
on the surfaces sho'wn edgewise at AB, AC and BD, locations are given relative to these surfaces. Thus inside 
distance between end arms of of", distance from end of aim to inside of back 2j", distance of ear from inside 
of end arm If". Dimensions of thickness, length and width of ear are given. Location of bolt holes is given 
from surfaces AB and BD. Specification of size and pitch of tap is given. Note that a drilled hole is 
located by its center, because it is necessary to prick punch a pomt on the metal to take the point of the drUl 
in starting. See also Section 27. 

40. An inspection of this drawing shows that the Yoke is composed of four parts. Dimensions had to 
be provided therefore, to give the size of the different parts and to give their relative locations. This is true 
of nearly eveiy piece used in a machine or structure. 

41. The drawing of the Pulley, Fig. 9, will illustrate the dimensions needed for a casting. As the Hoist 
Arm Yoke was dimensioned for the blacksmith and the machinist, so here the pullej- must be dimensioned for 
the pattern-maker and the machinist. The pattern-maker will need diameter, face width, thickness, crown- 
ing and draft for the rim; diameter of bore, diameter, length and draft on the hub; number of arms, section of 
arm, width and tliickness of arm at rim and at hub; relative position of hub and run and dimensions of rib at 
root of the arms. To allow for finish the surfaces to be machined are to be marked /. Note that the f is put 
on the surface where it projects as a line. 

The dimensions needed by the machinist are as follows. Diameter and length of bore, dimensions of 
keyw^ay ; diameter, face width and crowning on the rim. 

Fillets and rounded comers should be shown on the drawing, but the size is not usually dimensioned xmless 
they are of large radius and of importance in the design of the part. 

On small pulleys the inside diameter of the rim is often given, instead of rim thickness. 

42. The Spiral Gear Shaft, Fig. 9, illustrates dimensioning for a piece turned from round stock. Here, 
all the dimensions are for the machinist. An overall dimension tells him how long a piece of stock to cut off 



'26 

and avoids the necessity of his adding the partial dimensions. This piece is made up of cylindrical sections 
of various lengths. The diameter and length of each is given. Where a section is ground to size, the same is 
specified and it is noted that one part is ground standard, that is to exact gage, another is finished a half- 
thousandth large, while a third is ground one and one-half thousandths small. The length, diameter and pitch 
is given for each threaded part, also the kind and size of each key. No finish, as such, is specified because the 
shaft has to be machined from a much larger piece. If a large spindle or shaft were forged approximately to 
size before machining, then of course, finish marks would be used. Note also the discussion on these dimensions 
in Section 38. 

43. An illustration of the dimensions necessary for a part which has been standardised commercially 
is the Cap Screw or Tap Bolt of Fig. 10. Unless something irregular is required in the thread or head, it would 
be sufficient to give the diameter, length under head to extreme point and length of threaded part. See also 
Chapter III on Miscellaneous Details for other examples. 

44. A dimension line consists of two arrows with their shafts in the same line and their points 
terminating on the lines between which the measurement is taken. The measurement which is given 
by the figures is from point to point of the arrows. The following rules and suggestions give the general 
practice with regard to character and placing of dimension lines and figures. Figures 8, 9, 10 and 16 furnish 
illustrations. 

Note exception to this in Section 173. 

45. Dimensions should not be crowded on a projection nor around it to such extent as to make the read- 
ing difficult. 

46. To distinguish dimension lines from the outlines of the projection, make the former about one-half 
the width of the latter. Dimension lines are often made with red ink, so as to produce contrast in the blueprint 
between them and the lines of the projections. 

47. Make arrows sharp pointed and not blunt. 



48. If there is not space for the dimension on the projection, it may be carried to one side by extension 
lines as in Fig. 8, C. 

49. Draw extension lines first where they are needed, then the dimension line leaving a break near its 
middle (or at one side when necessary) for the figures. Put on arrowheads next and figures last. 

50. If the space for the dimension is ver^- limited \ise one of the methods shown in Fig. 8, C. 

51. Extension lines should not quite touch the lines they extend, as they would become confused with 
them. 

52. Extension lines should be of the same weight as dimension lines. 

53. A line of the projection must never be used as a dimension line. 

54. A center line must never be used as a dimension line. 

55. When the dimension line gives the radius of an arc, use an arrowhead at the arc end only. See 
Friction Pawl Shoe in Fig. 9. 

56. "^Tien several dimensions are parallel, the longest is placed furthest out to avoid confusion of exten- 
sion and dimension lines. See Cylinder Cap, Fig. 9. 

57. Dimension lines for an angle are usually circular arcs with centers at the vertex of the angle. See 
Fig. 16. 

58. Dimension figures give the actual size of the measurement indicated, although the drawing may 
be much smaller than full size. See Pulley, Fig. 9. 

59. Dimension figiu-es should read with the line and from the bottom or right end of the sheet for hori- 
zontal and vertical dimensions. For oblique dimensions, practice varies, but some draftsmen put aU such 
figures horizontal. 



28 

In the case of explanatory drawings for tables we have an exception to the general rule. See tables at 
the back of the book. 

60. Figures must be large enough to be perfectly legible in the blueprint which is often made from the 
drawing. They should be very distinctly formed. If space is too limited, take the figures to one side with an 
arrow to indicate where they belong. 

61. The division mark for fractions should be parallel to or in line with the dimension line. 

62. Many draftsmen specify all measurements up to 24" in inches and those above 24" in feet and inches. 
Practice is quite variable in this matter and diameters of turned forms especially are often given in inches even 
though of very large dimensions. Thus, a 32" shaft, a 72" pulley, a 54" cylinder. 

63. If all the dimensions on a sheet are in inches, the inch mark on figures is often omitted. 

64. If some dimensions are in feet and inches, then the foot and inch marks should be used and the 
figures separated by a dash. Thus, 2'-7", 3'-0", 7 ft.-5". 

65. If the size of a fillet or of a rounded corner is of importance, its radius should be given as in the Pulley, 
Fig. 9, the figures being followed by the letter II or by Rad. 

66. If the whole of a dimension line is not shown, some specification must be added to explain its extent. 
Thus in the Pulley, Fig. 9, the figures for the diameter are followed by Diam. 

67. If the size of a part is changed after the drawing is completed, it is customary to change the dimen- 
sion figures, but not the projection. For instance, suppose the hub diameter of the Worm Gear in Fig. 16 were 
changed to ly. Cross, but do not erase the IJ" and specify below, "changed to IJ"." 

68. Dimensions for angles may be specified by the number of degrees and tenths or by the amount 
of vertical rise on a given length of horizontal base. The former should be used where the measurement is to 
be made with a protractor, the latter is generally more convenient for the pattern-maker and is always used for 
structural work, and the pitch of pipe lines. See Fig. 19. 



29 

69. Dimension figures should never be crossed by a line, nor placed so as to interrupt a line of the pro- 
jection, nor an extension line. Note also the break in section lining about figures and lettering. See Figures 
9 and 16. 

70. Give diameters of circles and the radius of a circular arc less than a semi-circle. If the location of 
the center of a circle or arc is not indicated by lines of the drawing it should be definitely located and dimensioned. 

71. Do not duplicate a dimension given in another view, except for purposes of identification of a part 
othen\-ise not easily distinguished. 

72. Dimensions should be placed where they will be found quickly by the workman. They can gener- 
ally be arranged in natural groups and should be put on one view as much as possible. Thus in the Pulley, 
Fig. 9, all the hub and bore dimensions form a group and are on the same view. The keyway dimensions are 
sho^^'n in the view where all can be put on. For the lengthwise partial dimensions on the Spiral Gear Shaft, 
Fig. 9, an arrangement very nearly in a straight line is desirable. 

73. Supplementary to the dimensions is the printed matter that accompanies the drawing. The name 
of the piece, usually some identification number or sjmibol, the number of pieces required for one machine or 
structure, the material, the kind and extent of finish, heat treatment such as tempering and any other pertinent 
and necessar}^ facts are grouped together above or below the drawing to form a sub-title. See Figures 9 and 16, 
for examples. 

74. Notes are also added to explain special details, but these should be exactly definite and as few as 
possible. See notes on Bevel Gears and Spiral Gears, Fig. 16. 

75. Drive, force and shrink fits should always be specified. 

76. If a piece is hardened, tempered, case hardened, blued, nickled or oxj^dized it should be noted. 

77. Specifications are often made by gi\ing name of manufacturer or the trade name or number by 
which he designates a machine or part. Thus, No. 825 Ley Bushed Chain. 



30 

NOMINAL SIZES 

78. Specifications for much of the material that is used in construction are given by gage size, nominal 
size or size of one or more important dimensions. Some of the commonest of these are as follows: 

Belting. — For leather belts, give width in inches and the number of thicknesses. Thus, a 6" double belt. 
For cotton and rubber belting, give width and ply. Thus, a 4"-3 ply rubber belt. 

Chain. — For hoisting chain, give the diameter of rod from which it is made. For transmission block 
chain, give the circular pitch and the width of block. Thus, pitch l"-width f". For transmission roller chain, 
give the circular pitch, the width between inner links and diameter of roller. Renold chain is specified by 
circular pitch and the nominal outside width. Under 1" pitch the actual exceeds the nominal width, but above 
that pitch they are alike. 

Drilled Holes. — When of small diameter give size by Drill Gage number. 

Hangers, Wall Brackets and Pillow Blocks. — These are designated by the diameter of shafting they 
support. The drop of hangers is also given. 

Machine Screws. — Give diameter by Screw Gage number. 

Pipe. — For standard wrought iron pipe, give the nominal inside diameter. See Table 3. For spiral 
riveted pipe give inside diameter and thickness by B. W. G. 

Pulleys. — Give diameter, face and bore in inches. 

Rolled Sections. — See Section 169 for I beams, channels etc. 

Rope. — Give largest diameter over strands. 

Shafting. — Turned shafting for transmission purposes is often designated by its nominal diameter, the 
diameter before turning. Thus, by 2" turned shafting would be meant shafting having an actual diameter 
of Itt"- To avoid all chance for error the actual diameter should always be specified. 

Sheaves. — Give the diameter at the pitch line of the rope. 

Sprockets. — Give pitch diameter. 

Sheet Metal. — Thickness is usually given by gage number or in thousandths of an inch. Plate is also 
designated by thickness in vulgar fractions, thus, ■j\"and by weight in pounds per square foot. 



31 

Tapers. — Specify by the number and the standard, thus. No. 16 B. & S. 

Tubing. — Give outside diameter and thickness by gage number. 

Wire. — Give diameter by \N ire Gage number or in thousandths of an inch. Wire used for electrical pvu-- 
poses is often designated by its area in circular mils. A mil is -fiyvir ^^ ^^ inch. A circular nul is the area of 
a circle whose diameter is one mU. 

Wire Cloth.— Give the niunber of meshes per lineal inch and the gage number of the wire. 

Wood Screws. — Give the nimiber by Screw Gage. 

79. Specifications for the common forms of fasteningSj such as are sho^Ti in Fig. 10, are given in 
Chapter III. 

LINES OF THE DRAWING 

80. The various lines used in working drawings are shown in Figures 9, 10, 16, 18, 19, 20 and 21. General 
practice is to make aU hues with black ink, but many draftsmen prefer red for all lines except those of the pro- 
jections, because the two sets of lines are thus easily distinguished in the di'a^ing and in the blueprint made 
from it. There are three features to be considered in determining the character of these lines. 

Thej- should be easdj- distinguished from each other in the original drawing and in the blueprint, and 
should not consmne too much time in the making. 

81. The visible lines of the object are shown by continuous or full lines not less than -^" in width for 
ordinal y drawings. 

Hidden lines of the object are represented by dotted lines not less than -^" in width. The length of 
dot will vary with the size of the drawing and length of the line. The space between dots or dashes shoiild be 
just long enough to show that the line is broken. The end dot should start at the fuU line, provided it does 
not thereby become a continuation of some other line. Otherwise, start the dotted hne with a space. See 
dotted lines in Bevel Gears, Fig. 16. 

Center lines may be fuU lines or of alternating dots and dashes. In either case they shovdd not exceed 

2 the width of lines of the projection. 



32 

Extension lines may be full lines or dash lines and of the same weight as center lines. They should not 
quite touch the lines they extend. 

Dimension lines are usually made as two long dashes with a break for the dimension figures. For long 
lines they may be several long dashes. Width of line should be same as for center lines. 

Shade lines should be at least twice the width of the lines of the projection. 

Other lines may be combinations of dot and dash lines. 

GENERAL ARRANGEMENT OF A SHEET 

82. The general arrangement of a sheet of details will be similar to that of Fig. 9. Each part with its 
projections, specifications, dimensions and sub-title should constitute a group somewhat separated from the 
others, so as to be easily picked out by the eye. 

83. The title of a sheet, described in Section 299, will usually be placed in the lower right hand corner. 
It will provide a variety of information according to the system in use. 

84. Near the title is often placed a Bill of Material similar to that in Fig. 9 and Fig. 19. It is to facilitate 
the work of order and cost clerks. Many prefer a different order by which the number of pieces required is 
given first and the name of the piece second. 

85. There are usually placed at the lower right and upper left hand corners numbers or symbols to des- 
ignate the sheet and its contents for convenience in filing, indexing and reference. 

REPRODUCING DRAWINGS 

86. Drawings are conuiionly reproduced for the shop by blue-printing. If a drawing is to be thus 
reproduced, it should be made on tracing cloth, a thin, translucent specially prepared linen or on thin paper such 
as linen bond. If tracing cloth is to be used, the drawing is first made on paper with pencil in the usual way. 
The tracing cloth is then stretched tightly over the drawing and thoroughly tacked down onto the board. One 
surface of the cloth is usually glossy and the other side dull. Both take ink equally well, but some prefer the 



33 

dull side as it can be pencilled on. Whichever side is used, the surface should be sprinkled with a little ground 
chalk and rubbed over with a cloth. This is done to remove greasy places which do not take the ink well. The 
drawing is then inked as if on the original sheet. The natural tendency is to use fine lines on a tracing, because 
it is so easy to make them. This is entirely wrong as the fine ink lines do not print out clearly, unless they 
have been made with hand ground ink. It is therefore best to use the heaviest ink line possible and this will 
be determined by the closeness of lines in the smallest details. 

If thin bond paper is used, the drawing is pencilled and inked in the usual way. 

87. To print, the tracing or bond paper drawing is put in a printing frame with the ink lines next to 
the glass and the prepared print paper is laid on it, the sensitized surface being put against the drawing. The 
drawing is now exposed to the sun and allowed to print imtil it is possible to see just the least discoloration 
under the ink lines. This part of the sensitized surface having been protected from the light should retain its 
original color. The print is taken from the frame and washed thorouglily in a sink of clean water for about a 
half hour after which it is rinsed and hung up to drj'. 

88. The beginner nearly always overprints and thus gets poor lines. If the paper is fresh and the 
exposure is right, these should be a clear white. In washing the print, be careful that air bubbles do not coUect 
on its surface as they wiU cause spotting. Also be careful not to spatter wash water on the di'awing as it causes 
stains which cannot be erased. 

89. It is sometimes desired to make alterations in a blueprint. The white lines can be obliterated by 
ruling them with blue ink. White lines can be made on the blue surface by using a solution of conmaon washing 
soda in the pen instead of ink. 

90. Another process, known as the negative-positive process is sometimes used when it is desired to 
get prints just like the original drawing instead of reversed in color. In this process, a special paper is used 
which requires more manipulation than the common blueprint paper. Briefly, the method is this. The draw- 
ing is put in the frame, its blank side against the glass so that the sensitized surface of the print paper comes 
next to the ink lines. The resulting print is negative in color and reversed in position. After developing, fixing. 



34 

washing and drying, this negative print is put in the frame with its printed surface up so that the sensitized 
surface of a fresli piece can be in immediate contact with it. The print obtained this time is reversed in color 
and position with respect to the negative and is therefore like the original. By this process it is possible to make 
sharp, clearly defined prints even from drawings which are on heavy and almost opaque paper. The exposure 
is of course a prolonged one. Ordinary blueprint paper, if fresh, will give fair prints by tliis process. 

CHAPTER III 

MISCELLANEOUS DETAILS OF CONSTRUCTION 

91. Many of the simpler parts used in construction are common to all or most machines and structures. 
These will be considered at some length in the order of their arrangement in Figures 8, 9, 10, and 11. 

TYPES OF SCREW THREADS FIG. 10 

92. The Sharp Vee is used to only a limited extent, as it is difficult to keep taps and dies for it in con- 
dition. The sharp edge of the V wears down and approaches the shape of the U. S. Standard Section. Its 
lack of clearance makes it difficult to fit, if cut in the lathe. 

93. The Sellers or U. S. Standard is like the Sharp Vee with the point of the triangle flattened | of the 
height, at top and bottom. This is the thread in common use in the United States. 

94. The International Standard adopted by the metric countries is not shown here. It is exactly the 
same shape as the Sellers thread except that the point of the V at the bottom of the thread is rounded yV of 
the height. This is an improvement over the Sellers section, in that it provides clearance and facilitates fitting. 

95. The Whitworth, or English standard, has an angle of 55° and the point of the V is rounded top and 
bottom ^- of the height. 

96. The Buttress thread gives a form of great strength where the load is always in the same direction. 
Its friction is low and it is easily fitted. It finds application in Bench Vises and Screw Jacks. 



Types of Screw Threads Con^ent/onal Screws 



Sharp Vea 

60^ 



S£LL£f!S OH U.S. STANO. V££-/^.H.-S/f^^LE 



CON\/ENTIONAL THREADED HoLES 




Fig. 10. 



36 

97- The U. S. Buttress is a modified form of tlie preceding used by the U. S. Government for breech 
blocks of guns and for armor plate bolts. 

98. The Square thread is used for power transmission screws where large pressures are applied. Its 
friction is low, but it is expensive to fit. Dimensions as given in the figure are modified a few thousandths of 
an inch to procure easy fits. 

99. The Acme thread is used for screws like the lead screw on a lathe. It has some of the good qualities 
of both the U. S. Standard and the Square threads. It is often called the Powell thread. Dimensions as given 
in the figure are modified a few thousandths of an inch to procure easy fits. 

100. The Knuckle thread is useful where a thread is liable to be bruised, as it will stand many knocks 
and yet work in its nut. 

10 1. Pipe Thread, not illustrated, has a 60° Vee rounded slightly at top and root, and a taper of 1 in 32 
measured on a radius. 

CONVENTIONAL SCREWS FIG. 10 

102. The true curve of the edge of a screw thread is a helix and this, of course, cannot be drawn every 
time a thread is represented. Various conventional representations are therefore used which show the thread 
with more or less accuracy and save the draftsman's time. Those shown at A, B, and C are the ones commonly 
used. The thread lines are drawn at a slight inclination approximately that of the actual thread of the same pitch. 
The spacing is also approximately true. Note that the short lines are made heavier. At C is a form, useful 
where the space will not permit the intermediate lines. 

103. In the Vee R. H. Single screw, the thread makes eight complete turns or wraps about the cylinder 
in one inch. It is therefore called a No. 8 thread o'* an 8 Pitch thread. The linear pitch of the thread is really 
I", or the distance between centers of two adjacent Vees. In the Sq. L. H. Sing, screw, is shown a thread in 
wliich the linear pitch is |". There are four wraps in one inch and it is called a 4 Pitch thread. 



37 

104. In tlie Square Double screw, two digtinct threads are wound on the cylmder, as mdicated. Each 
wraps around the cyhnder twice in one inch and each is really a 2 Pitch thread. The distance between adjoin- 
ing threads, however, is only I", so to avoid confusion, it is customaiy in the case of multiple threads to use 
the actual linear pitch of the thread or helix and designate it lead. So in this case, we have h" lead. 

105. However elaborately a screw is drawn, the pitch should be specified always. If it be irregular 
in any way, that is, if it be multiple threaded, or left handed, it should be so designated. 

CONVENTIONAL THREADED HOLES FIG. 10 

106. Here we have various ways of showing threaded holes, so as to save time and avoid the confusion 
of lines. A and D are not much used. Note the angle of 120° used to show the drill point. Note also that 
the depth of the hole is not measured to the drill point, but to the corner. If two parts are threaded together 
and then cut with a sectioning plane, it is necessary to draw the thi'ead. See Fig. 8, B. 

COMMON FORMS OF BOLTS FIG. 10 

107. Through Bolts are always used where possible, in order to reduce expense. In some cases, however, 
as on a steam engine cylinder end, it may not be possible to get at the head of a bolt on the back of the cylinder 
flange. In such a case, stud bolts would be used for holding on the cylinder head. A tap bolt is sometimes 
used for the same purpose, if the cylinder head wiU not be removed veiy often. Where a bolt of this kind is 
frequently turned in and out of a hole tapped in cast iron, the thread on the hole is quickly destroyed. Such 
a bolt is therefore most suitable for a permanent connection. 

108. The anchor bolt for concrete is to be placed while the concrete is yet plastic. The one for stone 
is driven into a hole that flares slightly at the bottom, the wedge spreading the end to fit it. 

109. If one view of a bolt head or nut is shown and then only for pictorial pui-poses, the hexagonal form 
should show three faces and the square form should show one face. There can be no question then as to which 
is intended. If one \'iew only Ls shown in a working drawing, show two faces for the hexagonal form and one 



38 

for the sciuare. This permits dimensioning the distance between fiats, a measurement the worliman will need, 
if the faces are milled. 

no. The needed dimensions on the stud bolt are shown. Nut and bolt dimensions follow no universal 
standard. They are most frequently made by the U. S. standard, the proportions for which are given in the 
drawing and in Table i. These values apply to both square and hexagonal forms. Note the appearance of the 
chamfer on head and nut. Its angle is 45°. Note also that the bolt points are either rounded or beveled at 45° 
and that the thread lines do not run to the extreme point. The length of a bolt is measured from under its 
head to its extreme point. The diameter and length of thread are also essential dimensions. Pitch of thread 
need not be specified on a through bolt, but it is necessary on a tap or stud bolt, so as to agree with the tapped 
hole into which it will go. 

111. The table on Standard Bolts and Nuts is the Franklin Institute or Sellers' Standard and is for 
rough bolts and nuts. Referring to the dimensions given in Table i, 

F = l-2-D +Y' for head and nut. Thickness of head=|. Thickness of nut=D. 
For finished bolts and nuts, 

F =^liD +yV'- Thickness of head equals thickness of nut — D — yV- 

The U. S. Government uses the rough standard for both rough and finished bolts and nuts so the same 
wrenches may be used on either. 

The Manufacturers' Standard follows these dimensions for bolts. 

F =1JD for heads. Thickness of head =^D-// for sizes I" to yV"; is -34" for f" and =D-i" for sizes 
r to 2". 

The dimensions of nuts will vaiy according to the manufacturer. 

SCREWS AND SCREW HEADS FIG. lo 

112. The terms "bolt" and "screw" are used interchangeably by so many people that it is difficult 
to distinguish between them. We may classify them roughly by saying that a bolt is a screw and a nut, while 
a screw is simply the one piece. 



39 

The ways of representing and dimensioning the commoner kinds of screws are shown here. For the Collar, 
Knurled, Fillister and Button head screws, the length is measm-ed from imder the head to extreme point. For 
the Flat head, however, it is the overall length which is taken. Most bolts and screws pull the parts they con- 
nect together. A Set screw acts by forcing them apart. For this reason it has to be case hardened, at least 
on the point. 

113. Many screws are turned out of bar stock and their diameters run on the conmion fractional sizes. 
They are called milled or cap screws. 

The sizes for cap screws given here are those used by the Worcester Machine Screw Co. For Square and 
Hexagonal head screws, the diameters from j" to f" \ary by 16ths, and from f" to IJ" by 8ths. The lengths 
from I" to 1" advance by Sths, and from 1" to 5" by 4ths. The thickness of head equals the diameter of the 
screw. The distance between flats is for the square heads J" larger than the diameter, on sizes up to |" diameter 
and j" greater on sizes above |". The distance between flats for the hexagonal heads is ^" greater than the 
diameter, on sizes up to y*^" diameter and J" greater on sizes above ^" diameter. 

114. Flat and Oval Fillister head screws from J" to f diameter vary by 16ths, and from f" to 1" by 
Sths. Lengths advance by -iths, from |" to 6". Diameter of head exceeds that of the body, on the J" and ^" 
sizes by -jV", on the i" and -f^'' by Y, 011 the f " and f^" by -f^" and on the others by I". 

115. Flat and Button head screws have the same range as fillister heads in diameter up to |" and in length 
up to 3". Diameters of flat heads are i", f", if", f", i", H", i", 1", W, If"- Diameters of button heads are 

7 ff 5 " _J_" 9 q air ^it l Zn 15" i /' 1 1" 
"3^ ; TT J T^ ! TT 7 8 > 4 > TT j IT ) ■*■ ) ■'-4 • 

ii6. Regular Set Screws are case hardened, have cup or oval points and square heads with a dimension 
between flats slightly greater than the diameter of the body. Diameters from \" to |" advance hy 16ths, and 
from I" to 1\" by 8ths. Lengths range from J" to 1" by 8ths, and from 1" to 5" by 4ths. 

117. Machine screws. SmaU screws are made from wire by upsetting one end for the head. Their 
diameters are therefore the wire sizes and are specified by the niunbers of the screw gage. These are designated 



40 

machine screws. See Machine Screw Gage and the A. S. M. E. standard for machine screws in Table 2. Com- 
mercial sizes of brass and iron Flat, Round and Fillister head screws are of these diameters by gage. Numbers 
2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 24, 30. Lengths from A" to f" vary by 16ths, from f" to IJ" by 8ths, 
and from 1|" to 3" by 4ths. 

118. Punched washers are designated by the largest size of bolt with which they can be used, and their 
thickness by Birm. Wire Gage. Cast iron washers are regularly dimensioned. See Table 6 for punched washers. 

119. A lag or coach screw is a large, wood screw made to be driven by a wrench instead of a screw driver. 
Necessary dimensions are as shown. 

These screws have square or hexagonal heads. From {" to f", the diameters advance by 16ths of an inch 
and from f" to 1" by 8ths. The lengths from V/' to 6" advance by half inches and from 6" to 12" by inches. 

120. The included angle ft)r flat head wood screws is 82°. The diameter of the head is approximately 
1.9 times the diameter of the body of the screw. The range of commercial lengths is as follows: Up to 1" by 
8ths, from 1" to 3" by 4ths, and from 3" to 5" by half inches. See Wood Screw Gage in Table 2. 

RIVET FASTENINGS FIG. 10 

121. There is a great variety of rivet forms and only the three common ones are shown. Diameter and 
length as indicated designate the size. Note how the length of the countersunk head type is measured. Pro- 
portions of heads vary, but are approximately as shown in the illustration. 

Button and Countersunk heads are used in structural work. Pan heads for boilers and Countersunk heads 
for hull plating. See also the chapter on Structural Drawing. 

KEY FASTENINGS FIG. 10 

122. There are three types of keys in common use as follows. A Taper key, such as is used for fasten- 
ing a pulley to a shaft so it cannot rotate nor slide on the shaft, fits on all sides and is driven in tight. If its 
small end is not accessible for driving oiit, then a Gib-Head key is used hke the one shown in the drawing. The 



41 

section under the head is commonly square. This dimension and the length under the head are sufficient to 
designate it. If it is not square, give width X thickness X length. 

123. The following commercial sizes are those of keys made by the Standard Gauge Steel Co. These 
keys are square at the large end and have a taper of |-" in 12". Size of large end varies from I" to 3" by 16ths 
of an inch. Lengths from 1" to 24" vary by half inches. Keys |" at large end range in length from 1" to 4" 
and 3" keys range in length from QV to 24". Gib head keys have a similar range. 

124. The second type of key fits on the sides and prevents relative rotation but not sliding endwise. 
These keys are commonly square and are dimensioned as in the drawing. The Whitney or Woodruflf key belongs 
to this class. Its size is designated by manufacturer's number, but the length and width are often given so as 
to show the size of cutter required. See Table i. 

125. The third form of key is the Feather key. This is usually rigidly attached to the shaft or to the 
hub, so as to permit sliding of the parts end^^■ise without its loosening. These keys are generally of greater depth 
than the other kinds. The depth or thickness of a key is its racUal dimension as it lies on the shaft. 

126. A Key is subjected to shearing on a longitudinal section. A Cotter is a similar fastening which is sub- 
jected to shear on a transverse section. Cotters are often called keys especially on the connecting rod of an engine 
where they are used to draw up the boxes. A cotter is tapered and is di-iven tight to draw the connected parts 
together. It may hold by friction or be held by a set screw. In specifying, use the dimensions shown in the drawing. 

127. A spring cotter or spht pin is not used for drawing parts together, but to prevent a pulley or nut 
from coming off a shaft endwise. After pushing the pin thi'ough its hole, the ends are spread thus preventing 
its working out. Diameter at the neck and length imder head to extreme point are the necessary dimensions. 
The range of commercial sizes of standard spriug cotters is as follows : Diameters from ^" to ^" vary by 64ths 
of an inch, from |" to V by 16ths of an inch and from J" to f" by Sths of an inch. Lengths from h" to 4" varj^ 
by 4ths of an inch and from 4" to 6" by inches. Pins -^" in diameter, range in length from J" to 2". Pins f" in 
diameter, range in length from 3" to 6". 

128. Note the dimensions and specifications for the coiled spring in Fig. 9. 



Sr/fAiQHT Co(//=i.iNq f^eouciNQ Coi/f! CAP 



Pluq 



Tee 



y BfiANCH 



Clboiy 



4-5" Elbovi/ 




43 
PIPE CONNECTIONS FIG. ii 

129. Ordinan- Standard wrought iron pipe is designated by its nomiaal inside diameter. Thus a 12" 

pipe is just 12" in internal diameter, whUe a |" pipe is .269" in internal diameter. See Table 3 for properties. 

Extra and Double Extra pipe are of the same outside diameter as Standard, so their inside diameters 

have no significance. The thi'ead for a pipe is special, standard for the various sizes and is never specified in a 

drawing. See Section 101. If a hole is tapped for pipe the specification is, 2" Pipe Tap, for instance. 

130. The term fittings applies primarily to the parts used for connecting the different lengths of pipe. 
Valves are not considered fittings. Sketches of the various fittings and their names are given in Fig. 11. Their 
use is explained in the sketch showing a pipe "layout." 

The size of a fitting or valve is given as that of the largest piece of pipe which can be screwed into it. 

A straight coupling connects two pipes of the same diameter, while a reducing coupling connects two 
pipes of different diametei's. !Many fittings are threaded right and left to permit of making connections on a 
circuit of piping. If the connection must be sometimes broken, it is better to use unions to complete 
the circuit. 

Elbows and bends pro\ide for changes in direction, while Tees, Crosses and Y branches provide for branches 
and for changes of direction. 

On a fitting with side outlets the main part is called the run. The fitting is always specified by giving 
first the dimensions of the run and then those of the outlets. In Fig. 11, Y, is shown how to designate a Tee. 

A flange union is used where the joint must be tight and the pressures are high, as on steam piping. Screw 
unions are used on the smaller sizes of pipe, especially for water pipe. 

131. The conventional drawing of a pipe "layout" shown in Fig. 11 may be fiuiher simplified by using 
single lines for the pipe and fittings. A riser is a vertical section of pipe. In a sketch of this kind, give dis- 
tances to center lines of pipe, the size of pipe, name and size of each fitting, kind and size of each valve, cock, 
drip, lubricator or other apparatus on the line. For an inclined pipe, give the vertical rise in a given horizontal 
distance. 



44 



TAPERED PARTS 

132. Tapered arms and hubs of pulleys, sheaves, gears and other wheels are designed 
of total taper per foot. This taper is usually given on a drawing, however, by specifying 
the dimensions at the small and large ends. See Pulley Fig. 9. 

Tapering arms of levers and handles are designated in the same way. See Binder 
Handle, Fig. 9. 

Tapered parts that fit tapered openings are 
dimension at one end and the taper in inches per 
Cotter inj[Fig. 10. 



usually specified by giving the 
foot. See Gib Head Key and 



Birmingham 




13 14 



IS 
O 



16 



.134 .120 
Fig. 12. 



.095 .083 .072 .065 



Taper of centers, tool shanks 

and pins is designated by giving 

/ — N x—-. ^ ^ the diameter of the small end 

\^_^ \_J \^ and the taper in inches per foot 

2S4 •^■59 .23& as measured on the diameter. 

See Fig. 8, B. 

A tapered hole is drilled, 
turned or bored and reamed. 
The drill diameter, taper in 
inches per foot and diameter at 
the large end are to be given. If some one of the numerous standard taper reamers is 
used, it should be specified. Thus, No. 3 Morse Taper. Brown & Sharpe tapers are 
commonly used in the spindles of milling machines and the Morse taper for the spindles 
of drills and lathes. The Jarno taper of ^" per foot and other special dimensions is 
being used by some manufacturers. See Table 4 for the B. & S. and Morse tapers. 

On account of the confusion regarding the measurement of tapers, many 
draftsmen prefer to make a supplementary construction showing just how the taper 



for a certain amount 
U.S. Stand, for Plate 



I 

5 
5 
7 
9 
// 
/J 



m 



.28125 



.25 



.21875 




03375 



16 VMMMVM/////7m .0625 

18 vj^M/frn'm'TTTTTm .05 

20 ^^^i_ .0375 

22 —i—^ £3125 

24 .025 

28 .0/5625 

Fig. 13. 

is measured. 



45 



GAGES 



133. So many gages have come into use for measm'ing the various kinds of wire and sheet metals that 
it requires an expert to keep them properly differentiated. A few of those most useful to the draftsman are 
given. In order that the sizes may become associated with the numbers, a lunited number of wire and plate 
sections have been given in their actual sizes or as near them as is possible with a printed figure. It should be 
remembered that the Birmingham Wire Gage is the Stubs' Iron Wire Gage and not the same as the Stubs' Steel 
Wire Gage. The Twist Drill and Steel Wire Gage is for twist drills and drill rods. It nmst not be confounded 
with the many other steel wire gages. See Figs. 12 and 13 and Table 2. 



CHAPTER IV 

TOOTHED GEARING 



AootNouM Line. 



134. If two cylinders revolving on parallel shafts are pressed together, 
one wiU drive the other by friction, if the resistance of the driven cylinder to 
turning is not too great. With great resistance, slipping will occur and to 
avoid this, projections may be put on each cylinder with hollows between to 
accommodate the projections of the other. If these projections and hollows 
are properly shaped, the result is a pair of toothed gears. The original 
cylinders are called pitch cylinders. In Fig. 14, the pitch line or pitch circle 
is the projection of the pitch cylinder. The part of the tooth outside this 
line is the addendum and the part inside, the dedendum. The length of pitch line between centers of two 
adjacent teeth measured in inches is called the circular pitch. The tooth width is measured in the same way 
on the pitch line, as is also the space width. Note also the fillet and the clearance. The working depth 
line shows how near the tops of teeth of a mating gear approach to the bottom of the space. Face of a tooth 
is the working surface outside the pitch line and the flank is the working surface inside. 




WHOLE. Depth 
Fig.l4. 




46 

135- Ordinary gears have a whole number of equal teeth and of equal spaces. If the number of teeth 
on a gear be divided by the diameter of the pitch circle in inches, the quotient is a number called the diametral 
pitch. Thus in the Spur gear Fig. i6, the number of teeth, 16, divided by 2, the number of inches in the diameter 
of the pitch circle, gives 8, the number of the diametral pitch. This diametral pitch is the one commonly used 
in designating the gear. It is useful to remember that Circular Pitch X Diametral Pitch =t. 

136. The circular pitch system of designing gears still survives in the case of heavy power transmission 
gears with cast teeth. There is no argument in its favor except that it saves the scrapping of large numbers of 
stock patterns and tooth forms constructed on that system. Of course, any system of gears tends to perpetuate 
itself, because generally only one gear of a pair breaks at a time and the owner must replace it with another 
of the same system or else throw away the remaining good gear. The diametral pitch system will doubtless 
displace the other in time. The circular pitches in most common use are as follows : From f" to 2^" by 8ths, 
from 2V to 4" by 4ths, and from 4" to 6" by halves. 

137. For cut teeth the proportions are as follows. 
Tooth Width = Space Width =-| Circular Pitch. 

Addendum Length = ^.^^^^^^^^ p.^^^ 

Addendum Length, _,, Tooth Width 
Clearance = ^ or Clearance = ^q 

Dedendum = Addendum + Clearance 
Fillet Radius =Clearance. 

In the case of Cast teeth not machined, the space width exceeds the tooth width by an amount called 
the back-lash. This provides for running in spite of irregularities of the teeth. 

Fig. 15 shows the actual sizes of gear teeth of the common diametral pitches. 

138. Tooth outlines are single curved or Involute, as in the Worm Gear, Fig. 16, and double curved or 
Cycloidal as in Fig. 14. 



Actual Sizes 

Table of D/AMcr/fAt P/tches , 


OF Gear Teeth 

wo CiKCULAK Pitch Eowmlents 


Diam.Pi. 


dr. Pi. 


DiamPi. 


Cir. Pi. 


Diam.Pi. 


Cir Pi. 


Oiam.Pi. 


Cir. Pi. 


? 


l.57r 


5 


.GZ8- 


12 


.PSZ 


2G 


.121- 


2y^ 


1.396- 


6 


.sz-^- 


14- 


.224-- 


28 


.112- 


2>4 


I.ZST 


7 


^44-9- 


16 


.136- 


30 


.105- 


2M 


l.lt-Z' 


S 


.393- 


16 


.m- 


32 


.038- 


3 


/.(M-7- 


9 


.J4-3- 


20 


.lb/- 


36 


.087' 


S>i 


.898- 


10 - 


.5/*- 


ZZ 


.14-3- 


40 


.079- 


4 


.785- 


II 


.286- 


Z4 


.131- 


48 


.065- 





-PcgJ^20 
^^^4R <^^48 



Fig. 15 



48 

139- The dimensions needed on the drawing of any gear are as follows. Dimensions for the pattern- 
maker, if a casting is used; dimensions to enable the machinist to tm-n up the blank, as the uncut gear is called, 
and dimensions necessary for selecting the cutter and setting up the work in the machine where the teeth are 
cut. Only those dimensions and specifications relating directly to the teeth will be mentioned in considering the 
following gears. 

SPUR GEARS FIG. i6 

140. Dimensions necessary for teeth are thickness and outside diameter of blank, number, kind and 
pitch of teeth. 

RACK FIG. 16 

141. A rack is essentially a Spur Gear with an infinite diameter. Give its length and width, the kind 
and pitch of teeth. 

BEVEL GEARS FIG. 16 

142. In bevel gears the pitch surfaces are cones. In the drawing they are shown as isosceles triangles 
DAB and DBC. The pitch circle on the pitcli cone, used for calculations is AB for the small gear and BC for 
the laigf, that is, the largest in each. 

Considering now the small gear only, note that a tooth tapers from its large end as at UAT toward the 
vertex, D, of the pitch cone. The dimensions of the large end of the tooth are the ones used in calculations and 
it should be observed that this large end lies in the surface of a secondary cone whose elements are perpendicular 
to those of the pitch cone. This cone VAB is called the back cone. The pitch diameter of the small gear is its 
largest pitch diameter i. e. 2". The number of teeth is 20 and the diametral pitch is therefore number 10. The 
tooth addendum length AT is yd" and the dedendum length AU is -g\"- The various angles and increments 
may be computed by trigonometry, or by means of Bevel Gear Tables. 

Thus, having the pitch radii of the two gears, BZ and DZ, the center angle of 29°.75 can be found. AD 
can be found as the hypothenuse of the triangle AZD. From AT and AD, find by trigonometry the angle ADT, 
which added to the center angle gives 32°. 58. The complement of this angle, 57°.42 is the face angle. From 



Spur GEiAFf 



Rack 



"31^ 1 < !] I ll 



^J\/^. 



Beimel Gears 

0/v£ Each — Mach. 3t. 



E ~ Shaft An(^l£ 

F- CENTEH AN0LE 

H- Face Anqle 
J - Angle or Edge 
L - Cutting Angle 

^M- BACKING 

P/TCH Cones 
ABD -BCD 



60°25 

60°25 
57?05 




L£AO -P. H- Swe. 

Fig. 16. 



so 

UA and AD determine angle ADU, which subtracted from the center angle gives 26°. 55 for the cutting angle. 

The angle VAZ is called the angle of the edge and it is equal to the center angle. The outside diameter equals 

pitch diameter AB, + 2 AT Cos. 29°.75. The cutter is selected for 10 pitch and for a number of teeth equal 

AV 
to the number of teeth of the gear, 20, multiplied byT-^" 

To size for teeth, the machinist will need the outside diameter, the backing, angle of the edge, face angle, 
face of blank. For cutting teeth, he will need the number, kind and pitch of teeth, the number of teeth which 
determines the cutter and the cutting angle. 

WORM GEARING FIG. i6 

143. If the teeth on a spur gear are turned slightly so their angle agrees with the thread angle of a screw 
having the same circular or linear pitch, the two will work together properly and constitute a simple form of 
Worm Gearing. The thread section of the worm is made like a rack tooth and the relative action of the teeth 
can be best understood by thinking of the worm as a rack. 

If a more extended contact between the thread of the worm and the teeth of the gear is desired, a mill- 
ing cutter is made which is almost an exact duplicate of the worm. This is run with the worm gear and shapes 
its teeth. Such a cutter is called a hob and when one is used, the teeth of the gear are often first roughed out 
with a rotary cutter set at an angle to agree with the thread angle. This operation is called gashing. 

All the dimensions relating to the tooth are calculated, but the outside diameter of the gear may be 
measured from the drawing. Dimensions should be given in thousandths of an inch. 

Dimensions for AVorm are, length, outside diameter, root diameter, lead and kind of meshing tooth. If 
more than one thread is used it should be specified. 

Dimensions for Worm Gear are, outside diameter, width and bevel of blank; throat diameter, radius and 
width of groove; number, kind and circular pitch of teeth; tooth angle should be given if the gear is gashed. 
Tooth dimensions are based on the fractional diametral pitch corresponding to the given circular pitch and in the 

usual way. The addendum length in these teeth is equal to — or .07958". 



51 
SPIRAL GEARS FIG. i6 

144. If instead of a single thread on the worm used with the worm gear, a large number of threads had 
been used, then the lead would have been greatly increased and the angle between the thread and the axis of 
the worm as shown in the projection would have greatly decreased. The threads on the wonn would then appear 
more like teeth than threads. The tooth angle on the worm gear would have changed accordingly and the result 
would be two similar gears in which the teeth were portions of threads of very large lead. Such gears are called 
Spiral Gears. 

In the case illustrated by the drawing, the center distance between shafts is 444"; the ratio of numbers 
of teeth on the gears is y, the shaft diameters are Ij" and cutters to be used in cutting the teeth are 6 pitch. 
The necessary dimensions are shown in the drawing. Note that the relation between pitch diameter, pitch and 
number of teeth is not as in other gears. 

145. In laying out a pair of spiral gears connecting two shafts at right angles, but which are not in the 
same plane, there will usually be some fixed conditions such as center distance of shafts, speed ratio of the gears, 
minimum or maximum diameters of the gears and a limited number of available tooth cutters. It will be nec- 
essary' to determine first the relation of these various conditions by a consideration of the pair of completed 
gears shown in Fig. 16. 

Let S = center distance of shafts. 

Wg=angular velocity of gear. Ilg=radius of gear. 

Wp =angular velocity of pinion. Rp =radius of pinion. 

Vg=pitch line velocity of gear. Tg=no. teeth on gear. 

Vp =pitch Une velocity of pinion. Tp =no. teeth on pinion. 

Yg=no. teeth determining cutter for gear. Z —diametral pitch of cutters. 

Yp=no. teeth determining cutter for pinion. 5=helix angle for teeth of pinion. 

Referring to Fig. 16, right hand view, imagine the pitch siufaces of the pinion and gear to be pieces of 
paper wTapped on the pitch cylinders. Cut the pinion paper on the back side along an element and the gear 



52 

paper on the front side along an element. Considering the two papers to be held tightly together at the point 
of contact of the two gears, let the papers flatten out into a single plane which will be tangent to the two pitch 
surfaces at their point of contact. The appearance of these two papers will be as shown in Fig. 17. 

The rectangle A-B is the developed pitch surface of the gear, the oblique lines being the center lines of 
its teeth. The rectangle C-D is the corresponding development for the pinion. The tooth center lines being 
helixes, become straight lines in the development. Line E-F is the development of part of a helix passing through 
0, the point of contact of the pitch surfaces. This helix is normal or i^erpendicular to the center lines of teeth 
on the gear and a corresponding helix, HK, on the pitch surface of the pinion, coincides with E-F when that 
surface is developed. E-F is therefore perpendicular to the developed center lines of the teeth. 

The number of spaces on the line A-B equals the number of teeth on the gear and the spaces on the line 
C-D equal the number of teeth on the pinion. From the figure, it is seen that the number of spaces on E-F 
and A-B are equal, while the number on H-K and C-D are also equal. 

When the front surface of the pinion moves to the right one tooth, or one circular pitch, of the pinion, 
its component motion along E-F is equal to one normal pitch. This motion causes the back side of the gear to 
move downward a distance equal to one tooth or one circular pitch of the gear and its component motion along 
E-F is equal to one normal pitch. 

Therefore 

V„ Circular Pitch of Gear 

-^ = = tang e 

Vp Circular Pitch of Pinion 

Soeed Ratio = — - = — -= — ^tang ^ and = — ^ 

opeca itatio ^^.^ ^^ ^^ t, Wp tang (9 R^ 



R 



p 



W R 
By composition, s = p — but R^ -|- R_ = S 

^ ^ 'W,+Wptange Rp + Rg " ' 



53 

S "^S 

and R_ = or Diameter of Pinion = 2R„ = — ,-,, 

p W ^ W (1) 

1 + _LLp tang e 1 + ^ tang 6 

In cutting the teeth, the work is fed in the direction perpendicular to E-F and the width of cut will be 

one half the normal pitch. The diametral pitch of such a cutter equals =7 

^ ^ ^ Normal Pitch 

or the Normal Pitch = — . Tp =the number of teeth on the pinion. 

Li 

Then HK = Tp X Normal Pitch = TpX — 

Li 

■K 

CD^2^Rp H^= =^=Sine 

" CD 2,rRp " 

or2R„ = ^^p — (2) 

'^ Z Sin e ^ ' 

T '?S 
Combining equations (1) and (2) 2R_ = „ ^^ ^ = ~ (3) 

L fern Q 1 1 **' n i n 

1 +-;^tang e 
"g 

146. Suppose the following quantities are given: 

W 
The cente" distance of shafts — S. The speed ratio — — ^. The diametral pitch of available cutters — Z. 

The angle Q should be 45° for best efficiency, but may be as small as 12° for light work with the gears 
running in an oil bath. The best range is from 20° to 45°. 



54 



The angle 6 must also be one that will permit cutting the teeth on the milling machine. 
The minimum diameter for the pinion will be determined by the size of its shaft and key. 
Tp must be a whole number and we see from Fig. 17 that if Tp is integral, Tg will be also. 

W 

Inspection of equation (3) shows that if S, Z, and — p are fixed, then values for e within its allowable limits 

Spiral Gears must be tried until one is found which when substituted in (3) will give a whole number 

for Tp and a satisfactory value for Rp. Inspection of Fig. 17 will suggest various 
graphical solutions. The niimerical solution is very tedious even when expedited by 
the slide-rule. Several solutions are usually possible, but the selected conditions may 
be such as to give no solution. In the latter case, the construction of a figure like 
Fig. 17 will generally show where the difficulty Hes. 

The numerical values for the diameters and tooth angles as given in Fig. i6 
are quoted from, "Worm and Spiral Gearing," by F. A. Halsey, because they were 
obtained with great accuracy on a calculating machine. 

Note that the tooth angle is the angle which the tooth helix makes with the axis of 
the pitch cylinder. It is therefore the complement of the angle commonly given as the 
helix angle, namely, the angle which the helix makes with the plane of the end of the 
cylinder. The tooth angle as specified in Fig. 16 is more convenient for the workman, as it 
is the amount necessary to set over the head of the milling machine for cutting the teeth. 

147. It remains to determine the number of teeth for which the cutter is 
selected. It will not be the same for the pinion and gear. For the pinion, it depends 
on the radius of curvature of the normal helix of the pinion, and for the gear, on the 
radius of curvature of the normal helix of the gear. 




D£f£LOP£0 Pitch Surfaces 
Fig. 17. 



It can be proved easily by geometry, that Yp 
results given in Fig. 16. 



Sin^e 



and Y„ = 



Cos^ Q 



The student should verify the 



55 

148. The pitch diameter is always given on a gear although it may be of no use to the machinist. It 
is necessarj', however, in deteniiining the center distance between the connected shafts, or for checking and com- 
puting parts of the gear. For gears with cast teeth, it is needed by the pattern-maker in lajdng out and setting 
teeth. 

The machinist, in cutting teeth, needs many dimensions not given, such as total depth of cut, addendum 
length etc., but these are seldom put on a di"awing of the natm^e here described. 

149. Spur gears are used to connect parallel shafts. Bevel gears to connect shafts not parallel, but in 
the same plane. Spiral gears are used to connect shafts not in the same plane and at any angle. Worm gear- 
ing to connect shafts not in the same plane, but at 90° angle. Bevel gears of the same size connecting shafts 
at 90° are called Mitre Gears. Bevel gears connecting shafts not at 90° are often called Angle Gears. 

-r 1 ^1 1 -^ X- f xi • 1 turns per minute of the driver , 

in each case the velocity ratio 01 the pair equals, equals 

turns per minute of the driven 

number of teeth on the driven -,^1 <• • xi^i 111 ^1 ^^u 

. In the case of worm gearing, a thread would be counted as one tooth. 

number of teeth on the driver 

REFERENCE BOOKS ON GEARING 

150. Essentials of Geaiing — G. C. Anthony. 
A Treatise on Gear "VMieels — G. B. Grant. 

Practical Treatise on Gearing — Brown & Sharpe Mfg. Co. 
Formulas in Gearing — Brown & Sharpe ]\Ifg. Co. 
Worm and Spiral Gearing — F. A. Halsey. 



56 

CHAPTER V 

STRUCTURAL DRAWING 

151. Shop drawings of structural details are similar to those used for machine construction, but there 
are some differences which will be noticed in this chapter. Many of these notes are based on the practice of 
the American Bridge Company, and the illustrations are in Figs. 18, 19 and 20. 

There arc two common methods of making shop drawings. By the first, the drawing is made so com- 
plete that templets can be laid out separately on the bench for each individual piece. The Plate Girder, Fig. 
18 is an illustration of this method. 

152. By the second method, the drawings give only sufficient dimensions to determine the position and 
length of the main and secondary members, leaving the details to be worked out by the templet maker on the 
laying out floor. The Roof Truss, Fig. 19 is an illustration of this method. In this case, the working or gage 
lines, U-Y, V-X, X-Y etc., would be laid out on the floor with chalk lines actual size, for the entire truss. These 
lines give the lengths and bevels for the different members. For instance the size, shape and rivet spacing for 
the gusset plate at the joint X can be drawn on the cardboard commonly used for such a templet by reference 
to the lines meeting at X. The templet for the angle V-X would be laid out in a similar manner by laying it 
beside the line on the floor and marking off its length and the points for rivets. Such a templet would be made 
of a long, thin strip of pine one edge of which would be flush with the intersection of outside surfaces of the legs 
of the angle. The rivet center line or gage line would then be marked in its proper position on the strip, the 
rivet centers located and holes about Y in diameter bored for each rivet. An angle haying been cut to the correct 
length, the templet would be clamped in position on the outside of the leg to be punched. The workman then 
takes a prick punch which fits the holes already bored in the wood and prick punches on the angle the center 
of each rivet. The angle then goes to have the rivet holes punched in the machine. The punch used in this 
machine has a feeler on the end which, catching the prick punch mark, centers the angle relative to the punch 
so that the resultant hole is properly placed and with a minimum expenditure of time. Such a punch is shown 
in an inverted position at K, Fig. 31. 



Ope/? Holes —j^ Un/&SJ nof&c/. ._^ 
Stand. Gayei " " ^S 



zy&TfiTiTidz^ii 3 s -te^'.i'-*' li'ii'i ss^'^z-o" iiiiiii a@3'=z'-o' lizi'iiziz 4 



?» 



<>— ^— — 0t 



n^ 



=0^- 



0|L.,^_O ^ 



i^t: 



zSh 



-e e — r » 



o • " • o 



1=1- 



60-0 c fo c of Bearings 



J— f 



'^nH IZe2i=Z'-0' iflji'. I3<SZ'=2'-Z 3'3'li'ii ll&y=Z-9 



Sect/on of A— A 



lZji;Zj(4^iz?^l>i3{3 



Sole Plate l4'x§'x/'-8' 

plana/ on hotfom to ^ 

Z^'/g ^lolled Holes for Expansion End. 
/# dia. Holes for E/xed End. 




. Sole Plate 



¥ 



Inside, of Girder 



-Plate I'ff'i'/'-Zi 



•Coy. PI. /ajxi "46-/1' 

A 

Hi\f£f spacing same as Top 



« e Q Q — e — — gO Q — o 



-e — e- — -o — e — — o ■ 1 



H3 — e — e — — o — • — •A 



■ 4) O O -Q O e 



Flange 





60 Vr. Deck Plate Girder 



Fig. 18. 



58 

153- Though it is permissible to omit the dimensions for locating rivets in a drawing of this kind when 
the connected parts are shown in place together, such dimensions should never be omitted if the connection 
is to be made in the field. Thus, in the Roof Truss, the rivet locations are omitted for the gussets, but are given 
at U for the rivets connecting the end of the truss to the top of the column that supports it. 

154. While practice regarding the application of these two methods is not uniform, columns, plate 
girders, heavy lattice girders in buildings and chords, floor beams and stringers in highway bridges are generally 
laid out by the first method. Roof trusses, light lattice girders and complicated work such as towers, domes 
etc., are laid out by the second method. 

155- The common scales for details are |" and 1" to the foot, but for large plate and lattice girders, 
\" and f" are used. 

156. Members are shown as nearly as possible in the positions they occupy in the structure, the hori- 
zontal members horizontal and the vertical members vertical. If, because of lack of space, an inclined or vertical 
member is shown horizontal, it should have its lower end at the left. 

The top view is placed above the elevation. The bottom view is placed below the elevation. The bottom 
view is a horizontal sectional view as seen from above. 

157. Cut parts are cross hatched if large enough, otherwise they are blackened. If blackened, open 
holes for field connections are left white. See Fig. 10 and Fig. 18. 

158. Center lines or working lines generally coincide with the rivet gage lines. In Fig. 19 these would 
be U-Y, U-X, V-X and X-Y. Some draftsmen use the line of intersection of the backs of legs of an angle for 
a center line. A few use the line through the center of gravity of the section. Give the distance from the 
gage line to a finished edge. 

159. The bevel or inclination of one member to another is designated by a right triangle one of whose 
legs is usually 12" long. The principal use of bevels is in laying out gussets. See Figs. 19 and 20. 



59 

i6o. Heads of shop rivets are shown in the view where they appear as circ4es and seldom otherwise 
except for indicating clearance as in the case of the clip angle, Fig. 20. 

161. Open holes for field connections are always blackened except as noted in Section 157. 

162. Conventional Rivet Signs, Fig. 10, enable the draftsman to avoid covering his drawing with printed 
notes regarding the heads and points of rivets. They also permit a great saving of time. 

163. The dimensions of rivets commonly used on structural work are given in Table 5. In naval con- 
struction the diameters range from j" to 11". 

164. The location of rivet gage lines for the various sizes and shapes of sections has been partially 
standardised and these are given in Table 5. In the case of a line of rivets in a plate, the center line should be 
located from the finished edge if there be one. 

165. To provide space for the riveter die, a certain amount of clearance between adjacent rivet heads 
is necessary. These clearances for different sizes of rivets are given in Table 5. 

166. It has been foimd necessary to Umit the distance between rivet holes and the distance from a 
hole to the edge of a plate, for if it is too small, there is danger of fractiiring the plate when punching. Thus, 
the minimum distance between centers of holes is taken equal to thi-ee diameters and from the edge of a plate 
to the center of a rivet as one and one-half diameters of the rivet. These distances are usually shghtly exceeded 
in practice. Those commonly used are given in Table 5. 

167. In a single row of rivets, the distance between two consecutive rivets is termed the pitch. See 
for example the end cover plate on the Plate Girder, Fig. 18. In a double row of rivets, the distance between 
tw^o consecutive rivets in alternate rows measured parallel to the gage lines is termed the pitch. This is illus- 
trated in the top flange of the Plate Girder, Fig. 18. 

168. In a long row of rivets, it is customarj- to space them equally or to arrange them in groups of 
equal spaces. When so arranged, the spaces are dimensioned in groups instead of singly, thus, 5@3"=i'-3" 



Matehial for One Trus s 





Maak 


OEiCRIPTION 


Lensth 


4- 


T.C. 


^ J£'^i> i" 


l6-2^i 


2 


B.C 


^^i-erxi- 


z9-a' 


2 


Dl 


iS2-k''2i'''£ 


3-9~± 


2 


D2 


/i2'x£-x^- 


7-7it 


4- 


81 


PI. sf^ i- 


/■-i- 


2 


Q2 


P/. Si-'j^- 


/'-%■ 


2 


^J 


P/.9i>£' 


0--7^ 


2 


(?4 


PI. 9i'^4:' 


r~r 


/ 


G5 


PI /I 'A' 


I'-H 


6 


K35 


A ■f>J>,f" 


0'-7r 



Roof Truss 



Rivets - f 

Open Holes — j^ 

•Sfd. Qages un/e-ss no+ed. 

Paint - I Coat -Blach. 




Fig. 19. 



61 

means that there are five spaces three inches long and that they total a length of one foot and three inches. See 
Plate Girder, Fig. i8. 

In case of a double row of staggered rivets, they are often specified as follows. 7 alt. @ 4" =2'-^'. 

169. Structural steel shapes are designated as follows; 

For an I Beam give — depth of web X weight per foot X length. 

For a Channel give — depth of web X weight per foot X length. 

For an Angle give — length of leg X length of leg X thickness X length. 

For a Z Bar give — depth of web X length of leg X thickness X length. 

For a T Bar give — width of flange X depth of bar X weight per foot X length. See Fig. 10. 

170. Gusset plates are often designated by their thickness only as are those of the Roof Truss, Fig. 19. 
Their size is usuall)'^ given more completely by the width in inches X thickness X length in feet and inches of 

a rectangular plate from which each could be cut. The foUomng are examples. 15" X }" X 0'-9" 1" X |" 

X I'-O" 14" X \" X l'-2". The length is commonly taken as the dimension along the principal member to 

which the gusset is connected. 

171. Rectangular plates such as web plates and fillers are designated in the same way as gussets except 
that the longest dimension is usually taken as the length. See Plate Girder, Fig. 18. 

172. Lattice bars are designated thus — width X thickness X length center to center of holes. See 
Fig. 20. 

173. The customai-y way of putting on dimension lines and figures is sho^wn in Figs. 18, 19 and 20. 

The chief peculiarity noted is that the figures are placed on the side of the dimension line instead of in a space 
made bj^ breaking the line. This is rendered necessaiy by the veiy small space available for manj- of the dimen- 
sion figures. 

In a small size drawing of a part like an angle having thin legs which must be showTi by two lines very 
close together, it is not possible to use heavy lines. To distinguish between the lines of the figm'e and the ex- 



62 

tension and dimension lines really requires that the latter be made with red ink. This is particularly true where 
a blueprint is to be made. In the latter case, by using red ink the dimension and extension lines appear a 
light blue in the print and are easily distinguished from the white lines of the figure. 

GAGE LINES RIVET SPACING RIVET DIMENSIONS 

174. A word of explanation is necessary for Table 5. The dimensions there presented are not to be 
considered as standards which have been universally adopted by construction companies, but rather to represent, 
as nearly as possible, the prevailing practice. The dimensions of rivets, for instance, will be found to vary con- 
siderably, and there is no agreement among builders as to the minimum rivet spacing. Regarding the latter, 
it may be said that while the theoretical minimum space between rivets is three times the diameter, and the 
distance from the center of a hole to the edge of a plate one half that amount, these rules are not rigidly adhered 
to in practice. As has already been stated, these distances are usually slightly increased. The distance from 
the center of a hole to the edge of a plate should be equal to two rivet diameters if possible. The minimum 
distance may be slightly decreased if the edge referred to is a rolled instead of a sheared one. The clearances 
given in the table are not so generous as those called for by some builders and should be considered the real 
irreducable minimum. The dimensions for the gage lines on beams, channels and angles are more nearly stand- 
ard than those for the Z bars and T bars. The source of each of these tables is specified and the reader can 
use his own judgment with regard to them. 

DEFINITIONS OF STRUCTURAL TERMS 

175. Angle. — A rolled piece of steel whose cross section is L shaped. It is specified on a drawing as an L. 
Apex of a Truss. — This is the highest point, as Y in the Roof Truss, Fig, 19. 

Batten, Stay or Tie Plate. — A plate used at the ends of compression members to hold the two segments to- 
gether. See Latticing, Fig. 20. 
Bevel. — ^The inclination of members to each other. See Roof Truss, Fig. 19, 
Bottom Chord. — The bottom member of a truss, as U-X — , Fig. 19. 
Channel. — A I'olled piece of steel whose cross section is C shaped. It is specified on a drawing as a C. 




J 

- ' <\l CSJ <\J <\J 



Fig. 20. 



64 

Clevis. — A forked piece with a threaded hole at one end, used for connecting a pin plate to a tie rod. 

See Fig. 20. 
Clip or Clip Angle. — A short angle used for connecting two pieces. In Clip Angles, Fig. 20, a clip is used at A 

to provide enough rivets to transmit the stress from the gusset to the angle B without unduly enlarging 

the plate. At C, a clip is used to connect the roof purlin to the top chord of the truss. See also, Fig. 19. 
Coping. — As applied to steel work, this is the cutting of the end of a beam or channel to fit the contour of a 

beam or channel which it abutts at right angles. See Coped Beam, Fig. 20. 
Cotter Pin. — ^A pin with a head at one end and with a spring cotter at the other. It is also called a Lateral 

Pin. See Fig. 20. 
Cover Plate. — A plate riveted to the flange angles of a plate girder to increase the flange area. Also, a plate 

used to cover a part of a member which would otherwise appear unfinished. Both are used on the Plate 

Girder, Fig. 18. 
Crimped Angle. — ^An angle bent so as to produce a slight offset. They are used for web stifTeners and avoid 

the necessity for fillers. See Fig. 20 and note the specification regarding rivet spacing. See also Fig. 18. 
Eye Bar. — A rod or bar enlarged at the ends to provide for pin holes. The ordinary and the adjustable are 

sliown in Fig. 20. 
Field Riveting. — This is riveting which is done outside the shop, often by hand and under conditions which 

prevent the making of tight joints. 
Filler. — Material used to fill the space between connected parts so as to preserve the right distance between 

them. It may be a washer, a ring, a piece of bar or plate or sometimes a block of wood. Note washers 

between chord angles in Fig. 19 and plate under the web stiffeners in Fig. 18. 
Flange. — The part of a beam, channel, T bar etc., which carries the tension or compression stresses. See Fig. 10. 
Flats. — ^The common commercial designation of rectangular bar stock. 
Gage. — The distance of a row of rivet holes from some assumed base line. See Table 5 for gages commonly used 

for rolled sections. 
Gage Line. — The center line of a row of rivets on rolled sections. 



65 

Gusset. — A plate to which intersecting members are attached to form a connection between them. See Figs. 

i8, 19 and 20. 
Hitch Angle. — Same as chp angle. 

I Beam. — A rolled piece of steel whose cross section is I shaped. 

Lacing or Latticing. — A zigzag or crisscross arrangement of bars, called Lattice Bars, which are used to con- 
nect the segments of compression members. Both single and double latticing is shown in Fig. 20. The 

angles specified in the figure are usually the minimum employed. 
Lug or Lug Angle. — Same as clip. 
Open Holes. — Holes left for field connections either rivets or bolts. They are always blackened in the drawing. 

See Plate Girder, Fig. 18. 
Panel. — The space between two successive chord joints. In Fig. 19, the space between U and V constitutes 

a panel. 
Panel Point. — ^The intersection of a secondary member with the chord of a truss. In Fig. 19, U, V, Y are panel 

points. 
Pin Plate. — ^A plate riveted to a member and provided with a pin hole which permits a pin connection with an 

eye bar or with a rod and clevis. 
Pitch. — Pitch of rivets is the distance between two consecutive rivets of a row measured in the direction of 

the row. If there are two rows staggered, the pitch is the distance between two consecutive rivets in 

alternate rows measiu-ed in the direction of the row. See Fig. 18. 
Pitch of a Roof. — The pitch or inclination of a roof is expressed by the fraction obtained by dividing the rise 

or height by the span. The pitch in the roof truss shown in Fig. 19 is. -^ The pitches most commonly 

used are i, I and J. 
Purlin. — ^A purlin is a cross member attached to roof trusses and to which the roof covering is attached. They 

may be beams, channels, angles or Z bars. See Fig. 19. 
Secondary or Web Members. — These are the members between the top and bottom chords of a truss or girder. 

In Fig. 19 they are V-X and X-Y. 



66 

Separator. — ^This is a casting formed so as to fit the webs and flanges of two I beams which are placed side by 

side and is to preserve the spacing between them. See Fig. 20. 
Sheared Plate. — This is long wide plate which has been trimmed to a rectangular form from one with irregular 

edges. 
Shop Rivets. — The name for rivets driven in the shop. 
Sole Plate. — A plate attached to the end of the bottom flange of a girder to insure the distribution of the pressure 

on the bed plate and support. See Fig. 18. 
Splice Plate. — ^A plate used for attaching two rolled sections or plates which are butted together endwise so 

they shall act as one piece. See web splice, Fig. 18. 
Stay Plate. — Same as batten plate. 

T Bar. — A rolled piece of steel whose cross section is T shaped. 
Tie Plate. — Same as batten plate. 
Top Chord. — The top main member of a truss. 
Truss. — A framed or jointed structure designed to act as a beam and whose members are usually subjected to 

longitudinal stress only, either tension or compression. See Fig. 19. 
Universal Plate. — Plate that is rolled in a universal mill so as to produce finished edges. Such plate is very 

long and relatively narrow. It is especially adapted for such purposes as cover plates for girders. 
Upset or Upset Rod. — ^A round rod enlarged at its ends so it can be threaded without reducing its strength. 

It is used with nuts, clevises and turnbuckles. See Clevis and Upset, Fig. 20. 
Web. — This is the part of a plate girder, I beam or channel between the flanges and is designed to carry the 

shear. Fig. 10. 
Working Lines. — These are the center lines used in laying out the parts of a framed structure. They usually 

coincide with the gage lines. In Fig. 19, the working lines are U-Y, U-X, V-X and X-Y. See Section 

158. 
Z Bar. — ^A rolled piece of steel whose cross section is T. shaped. 



67 
PLAN OF BUILDING FIG. 21 

176. The plan of the Foundry Building shown in Fig. 21 illustrates the salient features of such a draw- 
ing. Note the following characteristics. Outside dimensions of the building are given, thickness of walls, 
center to center location of windows and doors, size of doors, location of columns, posts, partitions, and interior 
walls. Size of rooms is specified by measurements between the inside faces of walls and the center lines of 
partitions. The "up" and "down" of stairways is indicated relative to the floor shown. The permanent 
foundry equipment is also located. The plan presented here contains more details than are usually given. 

CHAPTER VI 

GENERAL SUGGESTIONS ON TECHNICAL SKETCHING 

177. In instrumental drawing exact measurements are made, but in free-hand work measurements 
are approximated by the eye and must be largely relative. Dependence on instruments will usually hamper 
the free-hand draftsman and a sketch that is partly free-hand and partly mechanical is unsatisfactory. It requires 
but little practice to draw free-hand lines that are fairly straight or parallel and irregular curves are drawn quite 
as easily as with instruments. A free-hand sketch, if not too complicated, can often be drawn in a quarter the 
time required for an instrumental drawing and an expert will often make a sketch before the other man can set 
his compasses. 

178. Some students draw with a pencil in one hand and an eraser in the other. It is interesting to watch 
them. They will draw half an inch of a line and immediately erase it, because of real or fancied error. This 
is entirely wrong. If the line looks wrong, leave it alone and draw another beside it, across it, or any way so 
it looks right. If this is wrong, let it stand and draw others. An ellipse thus drawn may look like a bird's nest, 
but the true line can be picked out of the collection, made heavier and the others erased. 

Inspection of sketches made by masters will show all this jumble of trial lines which they did not consider 
of enough importance to erase. 




Fig. 21. 



69 



Practice at the blackboard where a free arm movement can be had is good training. 



In 



^1 


— 1 — 
4- 


1 

Z 


h 1 

/ 

/ 
1 


^ i 

z 

1 


7 


IS 
if) 


Fx 






3 

1 


4- 

1 




,f 


<?L_ 


7 




S 

1 


\ 




-jW 



lyQ. J. Id/UUH-il^ C1;U UlU-- MJlC4\_'XVILfVJC4'l.\^ VVXH^J.*^ C4 1 X V^ V CtiJ- Xll llAV^ V V^IJLIVIIU VC*JX± P^"^ XAt*VA XO ^WV/VA U A CfcXXAXXigj 

drawing a straight line, think of the point to which the line is going rather than about the hand or pencil. Curves 
may be sketched in, by first spotting a few points in them. 

i8o. To get fair proportions in a drawing, both the relative length and the angularity of the straight 
lines nmst be carefully considered. To get proper lengths, let some line of the object be taken as a unit and 
compare all other lengths with it. Then check by comparison of various related lines. 
To make these comparisons with celerity, the draftsman should become familiar 
with the appearance of different fractional divisions of a line. Measurement in 
eighths is a familiar and useful one as they are easily obtained by continued halving. 
See hne AB in Fig. 22. Thirds, sixths and fifths are also useful. To get thirds, place 
the pencil at 1 on CD and some other marker at 2; then adjust until the divisions 
look equal. Sixths are obtained from thirds by halving. For fifths use two markers 
as at 3 and 4 on EF and adjust until the distance between them is half of each end 
space. Sevenths are obtained on GH in a similar way, the markers being adjusted 

till the distance, 5-6, between them is two-thirds of the left end space and equal 

to the right end space. 

181. Inclination of a line is generally approximated by comparison with a 
horizontal; sometimes with a vertical if more convenient. The eye can detect a 
small error in a right angle and in parallel lines, but for intermediate angles a large 
error will often pass unnoticed. Great care should therefore be taken with per- 
pendiculars and parallels. 

182. For estimating angles intermediate between 0° and 90°, we naturally 
halve the quadrant getting 45°. This is always readily tested, because it is a rise 
of one on a base of one as shown in Fig. 23. Another angle familiar to most drafts- 
men is the 30°. This can be tested by the fact that the short leg F-30 of the right triangle is one-half the 



Fig. 22. 



Fon £sT/MAr/NQ 

An<SL£S 
60° 




70 

hypothenuse B-30. By halving the 30° angle we get the 15°. Another familiar angle is the 60°. Here, the 
base BD is half the hypothenuse B-60. By halving the angle between 60° and 90° we get the 75° angle. All 
these angles are in frequent use in engineering work and the student should become familiar with their 
appearance. With the quadrant divided thus into six equal parts intermediate angles may be approximated 
with considerable accuracy. 

183. If the plane of a square is parallel to the plane of projection or to the picture plane, the corner angles 
will appear as right angles and the diagonals will bisect them in the drawing just as in the original. If the square 
is placed so all its edges are oblique to the plane of projection or to the picture plane, its projection will be a par- 
allelogram and its perspective a trapezium. The corner angles of these figures are not right angles and their 
diagonals do not bisect the corner angles. See Fig. 38, B, and Fig. 3, A. 

184. If the square is placed so one side is parallel to the plane of projection or to the picture plane, then 
the projection will be a rectangle and the perspective very nearly so. 

185. If an angle be placed so its bisector is parallel to one of the planes of projection, then the pro- 
jection of the angle on that plane will be bisected by the projection of the bisector. 

186. It is therefore very important to remember, that in constructing figures whose planes are not par- 
allel to the plane of projection nor to the picture plane, no use can be made of the actual angle between adjacent 
edges. 

187. A triangle should be constructed by drawing its base, its altitude, its vertex and last the oblique 
sides. To locate the altitude properly, note how it divides the base line. 

188. In the equilateral triangle. Fig. 24, the altitude bisects the base. Note that the altitude is 
approximately equal to | of the base. The vertices of the concentric triangle are on the altitude lines. To con- 
struct the triangle draw BC, mark its middle point D, draw AD, locate A and draw AB and AC. This 
completes ABC. To construct FGH, measure off DE as a fractional part of AD, draw FG parallel to BC, 



draw altitude CK and BL, locate F and G and draw FH and GH parallel to AB and AC 
may be located in the same way as FG, if the preceding construction gives poor results. 

189. In the regular hexagon, Fig. 25, the short diameter, FH, is approximately 
I of the long diameter, AB. A side is equal to ^ AB and the lines FH and GJ bisect 
AC and 
figure. 



71 

Or FH and GH 



CB. The veitices of the concentric hexagon are on the diagonals of the outer 



AD=DC^ CE=EB=±AB 
FH=-^ABapphox. '^ 




To draw the outer hexagon, draw AB, halve it, quarter it and 
draw FDH and GEJ. Locate F and H, diaw FG and HJ parallel 
toAB. Draw last AF, AH, BG and BJ, then check by noting if 
opposite sides are parallel and equal to one-half their parallel 
diagonal. The base of the nut in Fig. 42, K, was drawn in this way. 

190. Rectangular figiu-es are constructed without difficultj^ by 
sides directly. 




drawing their 



Their diagonals intersect at the center. 



Fig. 25. 



191. After the rectangle, the circle is the com- 
monest figure with which the draftsman has to deal. If 
it is remembered, that it can be inscribed in a square, it 




:tj^ 



will be easier to draw, whether it is shown as a true cu'cle or as an ellipse. 

In Fig. 26 a circle is shown inscribed in a square. It touches the sides at 
the middle points. It cuts the diagonals at a distance from the center equal 
appi-oximately to j"-jj of the half diagonal. To draw the circle, mark its center and 
spot four points as E, F, G, and H equidistant from it. These points are needed 
not so much to produce a good curve as to insure its proper location and size. For the concentric circle, 
similar points may be taken, the distance between the two curves being measured on a radius and as a 
fraction of the large radius. Thus in the figure this distance is \ of the large radius. 



Fig. 26. 




72 

192. Suppose a circle is placed so its plane is oblique to the plane of projection, or to the picture plane. 
It may be proved that its projection, or its perspective is an ellipse. The circle has an infinite number of diam- 
eters and one of them will be parallel to the plane of projection and project in its true length. This will be the 
longest diameter of the ellipse, or its major axis. In the same way, one of the diameters will project shorter 
than any of the others and this will be the shortest diameter, or minor axis of the ellipse. These two axes are 
perpendicular in the ellipse and the curve is symmetrical with respect to each. 

193. The projection of the concentric circle will give an ellipse similar to 
the first. For instance if the radius of the second circle is | that of the first then 
each radius of the inner ellipse will be f of the coincident radius of the outer ellipse. 
This is shown in the full lines of Fig. 27. Thus ON =f OF and OP =f OQ. 

_^^^ cj 

194. Returning to the circle described in Section 192, suppose a hne be drawn 

perpendicular to the plane of the circle at its center. This line will be perpendicular 
to every diameter of the circle, therefore perpendicular to that one which is parallel to the plane of projection 
and which projects as the major axis of the ellipse. By the principle stated in Section 184, the projection of the 
line perpendicular to the plane of the circle will be a line perpendicular to the major axis of the ellipse. 

This is one of the most important principles relating to the projections or perspectives of cylindrical forms 
and its common violation, through ignorance, results in disagreeable distortions. 

From this principle, it follows that a circle whose plane is horizontal will be represented by an ellipse 
whose major axis is horizontal. 

195. The principles explained in Sections 191, 192, and 194 apply to correct perspective drawings as 
well as to projections. In the case of concentric circles the perspective representation is slightly different. The 
inner circle is shown as an ellipse, but its center does not coincide with that of the outer ellipse. This is shown 
by the dotted lines in Fig. 27. The plane of the circle is below the eye. 

196. A square circumscribed about the circle of Sec. 192 will project as a parallelogram. The ellipse, the pro- 
jection of the circle, will touch the middle points of the sides and have its center at the intersection of the diagonals. 



73 



197- The major axis should alwaj's be drawn or unagmed when drawing an ellipse and the cur\'e should 
be made sjTnmetrical on it. Having both axes given, mark the center of the ellipse and then spot points for 
the fom* ends of axes. Draw the cur\-e through these four poiuts. 

198. Referring to Fig. 43, B, let the plane of the circle partlj- shown by the arc HLK be parallel to the plane 
of projection. Let equal di\'isions be marked on it as indicated. Now revolve the circle on a line, CH, coincident 
with its diameter, imtil it projects as the eUipse of wliich one-half is SHJ. Any di^'ision point as L on the circle will, 
during the revolution, remain in a plane perpendicular to the axis and the projection of L will be found some- 
where on a line LM perpendiciilar to CH. As the projection of L must also be on the eUipse, it wUl be foimd at M. 

It is seen, that equal divisions on the circle are not so on the ellipse, its projection, but that they shorten 
gradually toward the end of the major axis. This construction will give results of considerable accuracy, even 
though drawn free-hand, "^lien some knowledge of the rate of shortening is acquired, the construction may 
be dispensed with. The gear teeth in the dra-ning were spaced by the eye and not quite accurately, as the con- 
struction shows. It is true, however, that the error is scarcely noticeable. 

199. Having a circle and one of its diameters, if a chord be dra^^^l parallel to the diameter and bisected, 
a diameter through the point of bisection will be perpendicular to the fii^t diameter. 
Xow place the circle so its plane is oblique to the plane of projection and the pro- 
jection of the circle becomes an eUipse. The diameter and parallel chord project as 
parallels and the chord is still bisected. The projection is shown in Fig. 28. 

Ha\'ing an eUipse ABCD representing a circle, and a Une, 1-2, representing a 
diameter of that circle, to find the line representing a diameter perpendicular to 1-2, 
construct as foUows. Draw a chord S-i of the eUipse paraUel to 1-2, bisect it at 
and draw the required Une 6-7 through point 5 and 0, the center of the eUipse. 




Fig. 28. 



200. The draftsman should acquire famiHarity with the shapes of various eUipses. Several should be 
constructed accurately by the method shown in Fig. 28. Draw two lines AB and CD at right angles and inter- 
secting at 0. On the straight edge of a strip of paper or card, mark FH equal to half the desired major axis 



74 

and GH equal to half the desired minor axis. Place the paper so that F falls on the line COD and so G falls 
on the line AOB, then move the paper about, keeping F and G always on their respective lines. Mark point H 
on the drawing at its various positions and connect them. The curve will be an ellipse. 

201, Irregular figures are best drawn by plotting as shown in the line ES Fig. 45. Select a base line 
1-11 and divide it into equal parts. Erect a perpendicular or ordinate at each division point and measure off 
on it the required distance. 



CHAPTER VII 

SKETCHES FOR SHOP DRAWINGS AND ELECTRICAL SYMBOLS 

202. If it is desired to have a sketch accurate as to shape and 
size, it should be made on cross section paper. The kind ruled in y 
squares is preferable, though that ruled in I" squares is suitable for 
large drawings. 

If the piece has one or more axes of symmetry, these should be 
drawn first as center lines. If the piece has any prominent circular 
parts, the view showing them as circles should be drawn first. Thus, 
in Fig. 29, the lower view of the box cap is the one to be started first. 
The dimensions being given and the scale of the drawing being 
assumed as half size, draw a horizontal and a vertical center line through 
point A. Take the radius of the shaft and spot points B, C, D. 
Draw the semicircle BCD. Draw in succession BE, DF, GE, HF, 
JG, PK, LJ and MK. Spot points 0, N and P, and draw arc NOP. 
Draw LQ and MR, then proceed to the top view. Draw center line 
Z-Z, then 1-2 and 3-4. By referring to the lower view, spot points 
5, 6, 7 and 8 and draw in order 1-7, 8-3, 2-5 and 6-4. By referring to the lower view, spot points 9, 10, 11 











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Fig. 29. 



75 

and 12 and draw in order 9-10, 11-12, 9-13, 11-15, 10-14 and 12-16. Spot centers of bolt holes 17 and 18 and 
draw circles. Spot 19 and 20 and draw arcs concentric with the bolt holes. Draw verticals at 5, 6, 7 and 8 
to meet these arcs. Draw circle for oil hole. 

Return to front \-iew and by projecting verticall)- from the top view, put in dotted lines for bolt and 
oil holes and the recesses cut for the nut. 

The order of drawing lines may be varied to some extent, but that given \s"ill enable the draftsman to 
do the work expeditiously and in ink without previous penciling. This is the kind of sketch which a designer 
most frequentl}' uses in working out details. 

203. If the draftsman has to make a dimensioned sketch of a piece in place on the machine, a different 
procedure is advisable. The piece should be sketched, dimension lines and specifications added before any 
measurements are made. The purpose of this, is to avoid soiling and obliterating the drawing as much as possible 
There is little advantage in making such a sketch on ruled paper, as the drawing is made by the eye. 

204. The piece to be sketched is the Rocker Arm sho-mi in Fig. 30. It is covered with dirt and grease 
and cannot be removed from the macliine. Before beginning the sketch, look the piece over carefully to deter- 
mine its character. 

Draw first the view showing the hubs as circles. Put in center lines X-X and Y-Y the angle between 
them being estimated by the eye. Spot centers of circles and draw aU six beginning with the large hub. In 
estimating relative sizes, base the diameter of the large hub on the distance between its center and the left 
hand center. Base the diameter of the small hubs on the diameter of the large one. Base the diameter of 
each hole on its own hub diameter. Next draw hnes of arms basing the arm width on the smaU hub diameter. 
Proceed to the lower view, put in the center line Z-Z and vertical center lines for the holes. Mark on vertical 
center lines the lengths of hubs basing the measurement on the hub diameter. Draw ends of hubs, determining 
their side limits by reference to the upper view. In the same way, spot and draw the lines of the arms, basing 
their thickness on their width. Draw the vertical side lines of the holes and hubs. The arms being fiUeted 
into the hubs, there wiU be no intei-section line, but the shape of the joint may be suggested by a line, as 
shown in the drawing. By showing one-half the front view in section, the construction is seen at a glance, 



76 



otherwise, dotted lines must be used. 



RocKEFi Arm 

Oai£ - AlAL . //f o/v ~Pat.No.33'1- 



CO/f£ HoL£S 



Draw the outline of the arm section. Little draft is necessary on the 
hubs as they are short. 

Next draw extension and dimension lines, but put on no 
figures. Make the measurements systematically, so none may 
be overlooked. The following order is satisfactory: Distance 
between centers of hubs ; Angle of arms ; Diameter and length 
of each hub and hole; Width and thickness of each arm. Put 
on dimension figures distinctly and mark finished surfaces in 
the view where the surface projects as a line. Make the sec- 
tion lining last. Specify material, number required and the 
pattern number, if there be one. 

205. If dimensions are known, and a sketch is to be 
made with some accuracy as to proportions, a scale can be im- 
provised as shown in the drawing, if neither scale nor ruled 
paper are available. 

206. If sketches like the preceding are made in the systematic way indicated, they may be drawn directly in 
ink. The beginner should work with ink from the start, as it trains him to look ahead and plan his drawing. He may 
spoil a few drawings at first, but a spoiled drawing is usually one of the most instructive lessons a draftsman ever gets. 

CHECKING A WORKING DRAWING 

207. Even with the utmost care an error in a drawing will sometimes get by the checker and appear 
in the finished machine or structure. Such errors may often be remedied, but sometimes they prove very costly. 
All reasonable precautions to avoid them should be taken. Not all drafting offices check their drawings, but 
most of them admit the desirability of doing so. 

No general brief rules can be laid down for checking a design as so many things have to be considered. 
A few things that easily creep in unnoticed ai'e as follows : Interference of parts, as might happen with the 




Fig. 30. 




'i^ij/ 



Fig. 31. 



78 

feed handles on a lathe carriage; Holes that cannot possibly be drilled; Tee slots which the cutter cannot 
get into ; Surfaces which a planer tool cannot reach ; Castings with impossible coring. 

In checking a drawing, we shall examine to see if there are sufficient dimensions and specifications and 
if they are the right kind to secure correct construction. Important dimensions, such as center distances, should 
be scanned more carefully than others. Also we must compare corresponding dimensions of related parts to 
see if they agree. Thus the bearing on a spindle must agree with the bearing in the box. The diameter and 
pitch of a screw must agree with the same dimensions on the hole into which it goes. 

The logical method is to take each piece by itself and putting yourself in the place of the workman go 
rapidly in imagination through each step in the process of making. Examine systematically the location, dimen- 
sions and specifications of each part of a piece. Where overall dimensions are given, see that they agree with 
the sum of the partial dimensions. Compare dimensions of fitted parts with the corresponding dimensions of 
the related piece. See if finish marks are complete, also if material, number required and any special treatment 
is specified. 

To illustrate, take the Spur Gear in Fig. i6. Is it cast or cut from the solid bar? Are dimensions for 
the pattern maker complete? Look for blank diameter, face width and bore. Is the finish fully specified? 
Are the dimensions for the machinist complete? He will first chuck and ream a 1" hole, then he will put the 
blank on an arbor, turn it to 2^" diameter, and face up the sides to |" thick. The teeth will next be cut. How 
many? for setting the index. What number, kind and pitch of teeth? for selecting the cutter. The arbor is 
now knocked out and the key way cut on the keyseater. What is its size? Where is the shaft on which this 
gear is to be keyed? Is the bearing for the gear 1" diameter and |" long and is there a j'Xi" key? These 
questions satisfactorily disposed of, the drawing may be considered checked. 

Many variations of this method of checking will be found desirable depending on the type of work con- 
sidered. It should be done always systematically to insure that every item is covered. If there are tapped 
holes, all might be considered at one time, examination being made for location, diameter, pitch and depth. 



Symbols for Electrical Diagrams 



Direct Current Dynamo, Motor or 
Generator, as indicated hy 



lotor or /^~\ 

D,M,or6. ~^^J~ ^'^"'^+^- 



-^fflM^ Field. 




Single Phase. 




Palyphi 



^ase 



Synchronous Motor 
^■yr generator, as 
shoi^n by letter. 



e 




Three Phetse /ndiycHon Mofor. 



Tiyo Phase /nc/t/cf/on Abator. 



(^•^■/~~ Synchronous Conyerter. 



(^ 



Voltmeter. 






V\/attmeter. 



Watt- hour - me+er. 



Trar7sformer. 



-AAAAAr- Resisfcince. 



-AAAA/V Variable Resistance- 
^MaMSUH^ Heacfance. 
-\mmmr- variable Reactance. 



H: 



Condenser. 
Circuit Breaker. 



-• — •- 



— A 



Fuse . 

S.P.S.T. Switch -Ojoen. 

S.P.S.T. Switch-Closed. 

D.P5.T. Switch. 



D.P.O.T. Switch . 




l|l|l|l|— Battery 



'/■ 



Wires Crossing, but 
not in contact. 

tVires Crossin£f and 
making contact. 



Fig. 32. 



80 

EXERCISES ON SHOP SKETCHES 

208. The following exercises have been selected to give practice in the making of rapid shop sketches. 
They should be sketched to some suitable scale, with ink, on cross section paper and without previous penciling. 
Use different or more views if it is thought desirable and select necessary dimensions where they are omitted. 
After completing the sketch of projections, put on all the dimensions and specifications needed by the workman. 

1. — Center Rest Jaw, Fig. 41. 2. — Flange G, Fig. 42. 3. — ^Washer N, Fig. 42. 4. — Box Cap R, Fig. 
42. 5. — Tailstock U, Fig. 42, 6. — Drill Stop, Fig. 46. 7. — Solid Bearing, Fig. 47. 

Next, take the parts shown in Figs. 44 and 31, alternating so as to make first a sketch from a projection 
drawing and then one from an axometric drawing. 

vwv^ 



Polyphase Light and Powlk Ciucuit 




< rTT^ 



k I 



W 



Fig. 33. 

ELECTRICAL SYMBOLS FIG. 32 

209. To facilitate the rapid sketching of plans for wiring, some system of symbols for the parts occurring 
most frequently is often useful. The ones given here in Fig. 32 have been adopted by the Electrical Engineer- 
ing department of the Worcester Polytechnic Institute. Their application is illustrated in Fig. 33. 



81 

CHAPTER Vni 

GEOMETRIC PERSPECTIVE AND ARTISTS' PERSPECTIVE. 

210. The method of making a Geometric Perspective drawing has been described in Chapter I. It 
was there pointed out, that such a drawing should be viewed from a particular point only, if it were to correctly 
represent the object. 

If one stands with his back against a wall, his arms outstretched on it and his eyes looking straight ahead, 
it is possible to detect motion of the hands. But though the angle of vision may be 180° or more, the angle 
of distinct vision is certainly very small. In reading from a page held at the usual distance, the eye can see 
distinctly the word at which it is looking and indistinctly the word on either side. Beyond this, the ordinaiy 
eye does not see words distinctly enough to read them and has to be turned. 

If then, we are examining a long drawing, we do not stand close to it at its middle and turn the eyes 
or head so as to get an oblique view of its ends, but we move about and stand in front of each detail to be exam- 
ined. It is for this reason, that geometric perspective drawings, so made that the eye embraces a large angle, 
are distortions offensive to the eye. Such a drawing would appear correct and without distortions if viewed 
from the right point, but it would be difficult to locate this point for an observer and it would be an unnatural 
and unsatisfactoiy way of looking at the drawing. 

Referring to Fig. 4, A, it is impossible for the human eye to see the front face of a cube as a perfect square 
and at the same time see the top and side faces. If the cube is placed so one face is seen as a perfect square, 
no other face is seen and if the cube be turned sufficiently to show a top and a side face also then the front face 
changes its shape, the top and bottom edges becoming inclined. 

Neither do we ever see a horizontal circle as a tilted ellipse, and the apparent shape of a sphere is always a circle. 

The photographic lens gives a true geometric perspective image and if on account of confined space, it 
is necessary to use what is called a "wide angle" lens, these distortions may become very great. We shall find 
in such photographs many curious representations, such as a sphere appearing as an oval solid similar to a hen's 
egg. This is due, it should be remembered, not to any defect in the lens, but to the geometric perspective. The 
eye could see a sphere the same way, if the angle of distinct vision were great enough. 



82 



211. Artists' Perspective shows an object as the eye sees it. Its results are similar to what would be 
obtained, if a spherical surface were used for the picture plane in a geometric perspective, the eye being placed 
at its center. As only a very small portion of such a surface may be considered approximately flat, the angle of 
vision is of small size. A panoramic photograph is a near approach to an artists' perspective, but inspection of one of 
these, shows new misrepresentations. The perspective is violated seriously in the matter of convergence of lines. 

It is therefore the province of the artists' perspective to harmonize all these incongruities and produce 
a drawing which, though not scientifically correct, produces a pleasing and satisfactory effect on the eye. 

212. We have seen in Chapter I, that a projection drawing is simply a perspective made with the eye 
at a great distance from the object. 

We have also noted the following facts about projection, namely. 

Lines oblique to the plane of projection do not project in their true lengths, but are foreshortened. 
The angle between two lines does not project in its true size, except under certain peculiar conditions. 
The projections of parallel lines are parallel. 

Equal divisions on a straight line will project as equal divisions. 

Lines parallel to the plane of projection project in their true size and shape. 

Equal and parallel figures project in equal and parallel figures, though not 
the same as the original. 

It remains, to discover how these results will be changed, when the eye is 
brought close to the object. 

Shohteiming of 

ouAL SPACES 213, The following principles are based on observation, but they may be 

proved by geometry. The line of sight is the line along which the eye looks at the 
object, just as in aiming a gun. The picture plane is always perpendicular to the line of sight. 



CON^Ef^GENCE 
OF fi9/f/ILi.£LS 




Fig. 34. 



214. In Fig. 34, is shown a ladder lying on the ground. Observe that lines which are parallel in the 
object, converge in the drawing. Fig. 41 shows the effect of non-convergence. 



83 



215- Comparing the convergence of the rungs with the convergence of the sides of the ladder, observe 
that the nearer lines are to being parallel with the line of sight, the greater their convergence. 

216. Parallels which are perpendicular to the line of sight show no convergence and if equal in length, 
the one furthest from the eye appears shortest. 

217. Exception. Though vertical parallels may appear to converge, they never are drawTi so. See 
Section 6, and Fig. 3. 

218. In Fig. 35 is a Geometric Perspective drawing of a regular hexagon resting flat on a horizontal 
plane. Two opposite sides and their parallel diagonal constitute a series of parallel lines. There are thus three 
series, each having its ovm direction. Note that the lines of each series converge toward the same point. This 
point is called the vanishing point of the series, because if the lines were imlimited in length, they would dis- 
appear at that point in the drawing. This may be seen on a long, straight stretch of railroad track. 

219. Note in Fig. 35 that the three vanishing points 
for the sides and diagonals are on the same horizontal 
line. 

All series of parallel lines which are parallel to the 
horizontal plane wiU liave their vanisliing points on the 
same horizontal line. This is called the Horizon Line. 



V.P.30°LEfT V.P4-S°L. 



EyeM 



f.P-i-S'/i. V.P30'ffiSHT 




A REGUI-AfI 

H£AA^OrJ /TESTS 

ON A HOff/^O.'^TAi. 

Pl-AN^ , A O/AQONAi. B£inQ 

PejT/'E'va/cui-A/r to tm£ 

P/CTL//f£ F'J^^E. 

Linear^ P£FtsPEcm^£ 

'Scale 5 jnch = I foor 



EYE. (M) 



Fig. 35. 



Each fAifir or Pa/^allel 

StOES CONVEfJ^ES TO A 
fO/fVT Otv THE Ho/TIZOr^ 
i.lH£. 



220. Notice in Fig. 34, that though the nmgs of 
the ladder are equally spaced, those furthest away appear 
closest together. 

If a straight line is divided into equal parts, those 
parts furthest from the eye appear shortest and the length gradually increases as they get nearer the eye. 
This may be seen in the spacing of ties on the railroad and on a picket fence. 

221. Fig. 36 is a drawing of three equal pulleys on a shaft . Note the difference in the shapes of the ellipses. 



84 



In a series of circles, the one whose plane is parallel to the line of sight appears as a straight line, the one 
whose plane is perpendicular to the line of sight appears as a true circle, while 
circles having intei mediate positions appear as ellipses with varying degrees of 
narrowness. This principle applies to other figures as well as to circles. 

It may be seen illustrated in long cylindrical forms such as boilers, tanks 
and pipes. 

222. With the exception of the variations stated in Sections 214 to 221 inclusive, 
the principles of projection drawings apply equally well to perspective drawings. 




P£/iSf£CTHi'£ 

OF PA/^ALLEL C/ftCL£S 



Fig. 36. 



MODEL DRAWING 



223. A course in model drawing from the object is of value for several reasons. It gives familiarity 
with the peculiarities of artificial type forms that are found singly or combined in all engineering constructions. 
It trains the faculty of exact observation. A drawing of a squash may be satisfactory, yet not much like the 
original. A drawing of a prism, a pyramid, a cylinder, a ring, a cone must be very nearly correct or the error 
is apparent to aU. Third, the outlines of such objects are not lost in complex light and shade nor in color effects. 

224. The following models taken in order will give a progressive set of exercises sufficiently comprehensive. 
Place them on the table or floor below the eye level and draw them in various positions. While doing this verify 
and apply the principles of projection and perspective which have been previously stated in Sections 212 to 221 
inclusive. A — Cube, B — Square Prism on end and on side, C — Square Frame lying flat and upright, D — 
Triangular Prism on end and on side, E — Triangular Frame lying flat and upright, F — Hexagonal Prism on 
end and on side, G — Hexagonal Frame lying flat and upright, H — Square Pyramid on base and on side, I — 
Hexagonal Pyramid on base and on side, J — Cylinder on end and on side, K — Half Cylinder on end and on 
flat side, L — Flat Ring lying flat and upright, M — Cone on base and on side, N — Sphere, — Hemisphere lying 
on flat surface and on cui'ved surface, P — Torus Ring lying flat and upright. 

225. When making a perspective sketch of an object, hold the drawing board in an upright position 
so its plane is perpendicular to your sight as you look down on it. It should be held low enough, so you can 



85 



look over its upper edge at the object and then back again at the drawing with only a sUght movement of the 
head. 

Before begirming to draw, read again Sections 212 to 221 inclusive and the suggestions in Chapter Yl 
and endeavor to apply them. Refer to them continually if you wish to be successful. 

Make j'our drawings of generous proportions. It may be easier to draw a short line than a long one, 
but it is more difficult to get proportions correct in a small drawing than in a large one. 

226. Suppose it is desired to make a sketch of the cube as shown in Fig. 37. 

Sit back in your chair in an erect position with the drawing board resting in an upright slanting position 
on the knees. When looking at or testing the Unes of the object, be careftil to occupy always the same position. 

Proceed in the following order. Draw verticals of indefinite length 
to represent the vertical edges of the right face. Estimating with the eye, 
decide on the relative horizontal widths of the vertical faces, then draw 
the left vertical of the left face. Take a point B on the middle vertical and 
judging the inclination by the eye, draw the top edge of the left face. In the 
same way, di'aw the top edge of the right face. The inclination of these 
lines may be more accurateh' judged, if the eyes are closed untU the lines 
are just visible. The draftsman may hastily conclude that the back edges of 
the top face appear parallel to the corresponding front edges, but careful 
scmtmy with partly closed eyes will prove the contrary- to be true. Having 
decided on their inclination, draw them, completing the top face. Next, 

estimate the length of the middle vertical, comparing with the horizontal width of the right face, 
its length and draw the bottom edges of the side faces in the same way as the top edges. 

The drawing should look prettj^ "scratchy" by this time if the instructions in Section 17S have been 
followed. 

227. Now test the drawing by comparmg lengtlis of lines and other suitable dimensions, and by 
measuring inclmations of lines. 




Fig. 37. 



Mark 



86 

Remember that it is the apparent lengths and not the true lengths of lines of the object which are to be 
compared. 

To compare lengths of the front edges of the top face, sit in the same position as when drawing them. 
Grasp the pencil at one end by the fingers of the right hand, leaving the thumb free to be moved back and forth 
on the projecting part of the pencil. Without moving the body, stretch out the arm straight to full length, 
then swinging the arm from the shoulder, bring the pencil so it appears near the right front edge of the top face. 
Now turn the hand, or the pencil in the hand until the pencil is perpendicular to the line of sight. Swing the 
arm slightly and rotate the arm in the sleeve until the pencil appears to coincide with the line, the end of the 
pencil being at one end B, of the line. Move the point of the thumb along the pencil until it coincides with the 
right end of the line. The length on the pencil from its point to the thumb is the apparent length of the line. 
Without removing the thumb, swing and rotate the arm so as to bring the pencil to lie along the line AB with 
its end on A. Be sure the pencil is perpendicular to the line of sight. Note now, how the point B appears to 
divide the length from the end of the pencil to the thumb. Is it one-half, three-eighths or what? Having decided, 
compare the lengths of the same lines in the drawing. In making these measurements the pencil must always be 
held at arm's length and perpendicular to the line of sight, or the results of the test will be worthless. 

228. To test the inclination of any line as AB, sit in the same position as when drawing the line. Place 
the board so its upper edge is horizontal and incline it until its plane is perpendicular to the line of sight. Take 
the pencil or a straight edge and lay it flat against the face of the board allowing several inches to extend beyond 
the edge as shown in Fig. 37. Look straight at the line AB to be tested and without moving the head, move 
the straight edge about on the surface of the board till it appears to coincide with AB. Holding it in this position, 
look immediately at the corresponding line in the drawing and note if it is parallel to the straight edge. After 
some practice in this way, it will be found accurate enough and quicker to judge of the inclination of the line 
by half closing the eyes and comparing with a pencil held horizontal. Then quickly place the pencil horizontally 
on the drawing next the line being tested and note if the angle is the same. 

Test the drawing until the correct lengths and inclinations are established, then remove superfluous lines. 
By using light sketch lines, this task will not be an arduous one. 



87 



229. "When drawixig cylindrical forms, draw the ellipse first after establishing the slant of the major axis 
and the ratio of lengths of axes. Then draw the straight side lines, being careful that their direction is such 
as to make the axis of the cyhnder pei-pendicular to the major axis of the ellipse. 

CHAPTER IX 

AXOMETRIC SKETCHING 

230. At Fig. 38, A, is sho^-n the projection on a vertical plane of a square 
parallel to it. Take an axis line X-X in the plane of the square and through its center. 
If the square be revolved on this axis until its plane is perpendicular to the plane of 
projection, its projection wiU be a straight line as shown at E. 

Intermediate positions wiU give projections as at B, C and D. 

In the original projection at A, draw the horizontal QR , the verticals MQ and OR . 

The triangles MPQ and OPR are equal and the following proportion is true. 

MQ PR 

= . When the square is revolved, these triangles change their form 

OR PQ 
in the projection, but it can be proved that the proportion is time for aU positions 
between the extremes mentioned. 

231. This fact gives at once a quick way for drawing the projection of a 
square which is oblique to the plane of projection. Referring to Fig. 38, C, let it be 
required to construct the projection of a square so placed that the ratio of horizontal 
distances between its three nearer comers is f. That is PR = 3PQ. 

Draw QR any desired length and take point P so PR = 3PQ. Erect verticals 
at Q and P. Draw ]MP at any desired inclination not greater than MP in A. Make 
OR the same fractional part of MQ that PQ is of PR, in this case J. Draw OP and 
MX parallel to it. Draw NO parallel to MP. Fig. ss. 




88 



232. If the true length of side of the square represented is desired, it can be found by noting from Fig. 
38, A, that it is the hypothenuse in a right triangle whose legs are equal to PQ and PR. 

233. In Fig. 39, the projection CDEF of a square has been drawn by the method of Section 231. AC = 
2BC and BD ='2AE. To complete the cube of which this square is the top face drop verticals at C, D and E. 
Draw trial lines for the bottom edges GH and HJ, placing them so as to make the figure look like a cube. Now 
turn the drawing around until CDIiJ becomes the top face and note if the drawing is still a good representation 
of the cube. It will probably be too tall or too short. Change the lines GH and HJ until the drawing looks 
like a cube in either position. 

The exact lengths of the verticals can be found by geometric construction, but the method described is 
sufficiently accurate and much quicker. 

234. Find the center K, of the top face by the intersection of diagonals and draw PT through it per- 

pendicular to CH. Mark the middle points of the sides of the top face 
and sketch in the ellipse which is the projection of the inscribed circle. Draw 
the ellipses for the other two faces, being careful to get the correct slant 
for the major axis. When completed, the three major axes should measure the 
same, if the work is accurate. 

Divide CE, CD, CH and PT into eight equal parts each. 

235. The three lines CE, CD and CH represent lines actually perpen- 
dicular and of equal length. They may be considered as axis lines of length, 
breadth and thickness. If the cube which this projection represents were a 
1" cube, then the projection of any other rectangular solid could be easily 
drawn by imagining the object placed with its edges parallel to those of the 
cube. Direct comparison could then be made between the lines in the 
Fig. 39. projections of the two objects. 




89 



A circle in any face of the rectangular solid would be represented by an ellipse of the same shape as that 
in the parallel face of the cube. The size of the eUipse would be determined by a comparison of its major 
axis directly with that of the ellipse in the cube. 

236, In Fig. 40 is a sketch made in the manner just outlined. The object is the Hoist Arm Yoke whose 
dimensions are given in Fig. 9. The drawing is made of small size by assmning that the reference cube used, 
that of Fig. 39, is 4" on an edge. 

At a point draw thi'ee axis lines OX, OY and OZ parallel respectively to lines CD, CE and CH of the 
reference cube. For convenience in measurement, lay off from on OX a length equal to l of CD, a length equal 



AxoMETWC Sketch 



ro f-CEr Cube.. 



/ 



to \ of CE on OY and on OZ a length equal to \ of CH. Each 
of these lengths represents an inch measured in the direction 
of its axis. These lengths are divided into quarters. 

Following the dimensions as given in Fig. 9, make OA 
7", OB 21" and OC 2". Draw CD paraUel to OA, AE and CG 
parallel to OB, AD and BG paraUel to OC. Make AE equal 
to OB then draw EH and FB parallel to OA and f " long. Draw 
HE, and FS parallel to OB and 2^" long. Draw RS paraUel to 
OA. Mark point J so that CJ equals 3i". Make JK |", KN 
li", and KQ If". Draw in order QP, JL, FN, PM, NL and 
ML, parallels to the lines of the ear first drawn. Make OU 1" 
and draw a parallel to OB through U. Make CT 2^" and draw 
a vertical through T. The intersection of these two lines is 
the center of the |" tapped hole. Draw the major axis of the ellipse perpendicular to OA and base its length 
on the line FT of the reference cube of Fig. 39. Draw the eUipse the same shape as that in the right face 
of the reference cube. The hole in the ear is located and the ellipse drawn in a similar manner. The 
shape of this ellipse will be like that in the top face of the reference cube and its major axis is perpendicular 
toOC. 




Hour Arm 



Fig. 40. 



90 



AX0/if£T/ilC 




M0Olf/£LO BY 
Of fA/iALLELS 



The projection of anj^ object, however complicated, may be drawn in this way, if its dimensions are known: 

As an endless variety of reference cubes can be constructed, it is always possible to select the most suitable 

position for representing the object. 

237. A drawing made in this way is called an Axometric Drawing, because the directions and measurements 

of lines are referred to axes representing the three principal dimensions of an object; length, breadth and thickness. 

238. If Fig. 40 is held at arm's length it looks correct, but from 
the usual distance of about 12" the further edges appear longer than the 
near ones and the lines supposed to be parallel appear to diverge away 
from the eye. Correct the drawing by shortening the lines until they look 
right and converge the parallels until they look parallel. In other words, 
modify the drawing, so it will not violate the principles of perspective. 
In Fig. 41 is an axometric drawing of a center rest jaw. Note that the 
back corner appears tilted up and the back end appears larger than the 
front end. The second drawing shows the axometric drawing modified 
by introducing convergence of parallels. Although changes in the drawing 

are slight, the change in appearance is marked. 

239. In Fig. 42, are shown a number of drawings of type forms made in the way just described. At R, is a 
box cap composed of a semi-circular shell with two ears. The complete elliptical end should be sketched in as indi- 
cated by the dotted lines, until the draftsman has become familiar with the appearance of the half cylinder form. 

240. In the case of truncated pyramid or cone forms, work with the vertex as shown in D and T. 

241. Where two irregular curves are placed symmetrically, draw the axis of symmetry first and plot 
the curves either side as in U. 

242. The nut at K was constructed by first drawing the complete base, then all the faces, last the ellip- 
ses and the contour at the right of them. To get the curve at the top of a face, plot its middle and end points. 
This is an Isometric drawing. 




Fig. 41. 




Fig. 42. 



92 

243- At H is a drawing of the Spiral Gear Shaft of Fig. 9. Draw center line first and mark centers 
of ellipses dividing into proper lengths by the eye. Draw ellipses, observing the perspective effect of distance, 
then draw the straight sides with convergence. 

244. Threads are drawn somewhat conventionally. A series of parallel ellipses with their major axes 
not quite perpendicular to the axis of the screw will be fairly suggestive of a screw thread. The shape of the 
ellipse should be the same as the end of the cylinder on which the thread is cut. Look out for spaces and the 
shape of the curve at the side line where it forms a slight notch. Threads are shown at D, E, G and H. 

245. At F is a rapid sketch of a coil spring. If done accurately, the point of the loop on the right would 
be horizontally opposite the space between points on the left. 

246. At G is half of a Flange Union such as S of Fig. 11. Draw the central ellipse first, then the four 
small ellipses representing bosses for the bolts. The centers of the four are on lines at right angles in the object. 
Apply method of Section 199 to determine these lines. 

After completing the upper ellipses, drop verticals and draw parallels to the upper curves. This is an 
axometric drawing without perspective modification. Note how the left side appears tilted, because of this. 
All of these ellipses have horizontal major axes. 

247. In the washer at N, sketch bottom ellipse complete before drawing side curves. 

248. At E is a straight coupling like A of Fig. 11. Note how the effect of a rounded edge on the end 
is produced. 

249. The character of a surface is often brought out by the curvature of lines on it. This is particularly 
true of spherical surfaces. Note this in the Binder Handle at S, Fig. 42. Observe that the major axis of the 
ellipse representing the flat place on the ball is perpendicular to a radius of the sphere drawn from its center. 

Straight lines for the slot on B would convert the curved top into a flat one. 

At C note that the outline of the hemisphere is made up of a semi-circle and a semi-ellipse. Also notice 
how the cui*ved lines of the slot are determined. 



93 

250. At Q, Fig. 42, is shown a torus ring, a form occurring in valve handles, hand wheels, pipe returns 
and bends. ^ 

If we take equal paper circles, each with a small hole at its center, and fill a wire circular hoop with 
them, we shall have a torus ring. Each circle will adjust itself so its plane is perpendicular to the wire at the 
point where it is situated. A projection of the wire hoop would be an ellipse, as shown in the dotted line in 
Q. Each paper circle would project as an ellipse. The major axis of each ellipse would be perpendicular to the 
curve of the wire i. e. to the curve of the large ellipse. Major axes of all the small ellipses would be equal. If 
all the small ellipses were drawn and a tangent contour to them made, we should get the outline of the 
ring. This outline is thus composed of curves parallel to the elliptical center line. One extreme position 
will show the ring as two concentric circles. The other extreme shows it as two semi-circles connected by 
parallel lines. 

251. If it is desired to draw a return bend like J of Fig. 11, draw the complete torus ring and cut 
it in halves as shown by dotted lines in Q, Fig. 42. To draw the small ellipse which represents the circular cut, 
draw the major axis perpendicular to the large ellipse curve at that point. A second diameter of the small 
ellipse, (not the minor axis) is found on the end of the oblique diameter of the large ellipse. From the relation 
of the lines the following proportion is true. 

Referring to Fig. 43, G, V-F is to V-G as D-E is to the major axis of the horizontal ellipse. 
If a quarter turn is desired, the ring may be divided into quarters in the same way and by use of the 
construction of Section 199. 

252. At L and M are shown chain and rope as they appear when hanging vertical. 

253. In sketches of sheet metal work, it is often desired to show the intersection of various surfaces. 
A pure guess will generally result in a bad representation, unless the draftsman is familiar with the different 
intersection curves. 

If the draftsman understands the construction of intersection curves by means of parallel cutting planes, 
the following method will prove useful. 



94 

In A, Fig. 42, is given a vertical cylinder whose axis is along 1-2. It is intersected by a cylinder whose 
axis 2-3 is perpendicular to that of the large cylinder at its middle point 2. The diameter of the small cylinder 
is one-half that of the large and its axis 2-3 is equal to the diameter of the large cylinder. 

Having drawn the projection of the large cylinder as desired, find the middle point, 2, of its axis. Draw 
the axis 2-3 of the small cylinder at any desired inclination. To find 3, draw 4-5 parallel to 2-3 and make 2-3 
equal to 4-5. Draw the major axis of the ellipse perpendicular to 2-3 and make its length half that of the 
ellipse of the large cylinder. To find a second diameter of the ellipse (not its minor axis), draw 8-9 a diameter 
perpendicular to 4-5 by the method of Section 199. Draw C-D parallel to 8-9 and of length equal to 8-1. 

In the actual object 8-9 is perpendicular to 4-5 and to 1-2, therefore perpendicular to the plane 1-2-3 E 
of the axes of the cylinders. The line C-D being parallel to 8-9 is perpendicular to the same plane, therefore 
perpendicular to the line 2-3. Line C-D must then be in the plane of the end of the small cyhnder. 

Draw the ellipse through points C, D and the extremities of the major axis, making it symmetrical on the latter. 

254. To find the intersection, draw first the line FEG which is the intersection of the planes of the ends 
of the cylinders. Cut both cylinders with a plane HJKL which is parallel to the plane of their axes. This plane 
will cut an element out of each cylinder, thus LH from the small and LK out of the large cylinder. These two 
lines intersect at point L which must therefore be a point common to both surfaces, or a point in their inter- 
section. Other points may be found in the same way. Three or four are usually sufficient including those for 
the side lines of the small cylinder. 

255. It may be objected, that the errors in making such a construction free-hand will give worthless 
results. Experience of many years use with beginners has proved the contrary. The method with all its errors 
will give results far superior to those of a guess and with a trifling expenditure of time. 

256. The Axometric Drawing gives us a rapid and accurate method for making a free-hand perspective drawing 
of an artificial object without the object or any drawing thereof, provided its construction and dimensions are known. 

The method briefly stated is this. First, construct a reference cube. Second, by comparison with it 
make an Axometric Drawing of the object. Third, change this Axometric Drawing into a Perspective Drawing 
by applying the common perspective principles. 



Sketches from Won king Drawings 




Fig. 43. 



96 

After the draftsman has followed this method for a time, he finds he can dispense with the reference cube 
and that he can introduce the perspective as he draws his lines. In other words, he has learned to make a per- 
spective sketch of an object not before him and can therefore reproduce in this way what exists only in his mind. 
Such ability is of the highest value to the designer. 

257. In Fig. 43 are rapid sketches of gearing which give a test of the application of the method. The 
least possible construction was employed in each case and most of this is shown in dotted lines. Auxiliary sketches 
indicate the way in which the drawings were built. 

EXERCISES 

258. Make Axometric drawings of the parts given in the following list, selecting one or more from each 
group. Those in Fig. 44 are drawn approximately to scale and if complete dimensions are lacking, the propor- 
tions should be as shown. 

Rectangular Prism Forms. — Square Frame, Fig. 48; Gib Head Key, Fig. 10; Cotter, Fig. 10; a short 
length of an I Beam, a Channel, an Angle, a Z-Bar and a T-Bar, Fig. 10; I Beam Connection, Fig. 48, M; a short 
length from the end of the Plate Girder, Fig. 18; Rack, Fig. 16; J,-0,-P,-V, Fig. 44. 

Triangular Prism Forms. — Triangular Frame, Fig. 24; Gauge Stop, Fig. 9; B,-D,-Fig. 44. 

Hexagonal Prism Forms. — Hexagonal Nuts, Table i ; Hexagonal Frame, Fig. 25. 

Cylindrical Forms. — Anchor Bolts, Fig. 10; Collar head Screw, Knurled head. Fillister head. Fig. 10 
and Table 2; Cylinder Cap, Fig. 9; Cotter Pin, Fig. 10; Pipe Plug, Fig. 11, D; Set Screw, Fig. 10; K,-S, Fig. 44. 

Hollow Cylinder and Ring Forms. — Ring, Fig. 48, D; Face Plate, Fig. 8; Washer, Fig. 10 and Table 6; 
Flange Coupling, Table 7; Eye Bar, Fig. 20; Blank for Spur Gear, Fig. 16; Pulley, Fig. 9; Pawl Friction Shoe, 
Fig. 9; Pipe Cap, Fig. 11, C; Pipe Flange, Fig. 11; Reducing Bushing, Fig. 11, N; Rocker Arm, Fig. 30; Blank 
for Worm Gear, Fig. 16; A,-C,-E,-F,-Q,-R,-Y, Fig. 44. 

Fractional Cylinder Forms. — Half Cylinder, Fig. 48, E; Woodruff Key, Table i; Box Cap, Fig. 29; Beam 
Separator, Fig. 20; Clevis, Fig. 20; G,-M,-W, Fig. 44. 

Intersecting Cylinder Forms. — Pipe Tee, Fig. 11, E, V; Y B^'anch, Fig. 11, F; Cross, Fig. 11, P. 

Divided Circle Forms. — ^Ratchet Wheel, Fig. 48, L; Spur Gear, Fig. 16. 





^/£Hi\^l 






Fig. 44. 



98 

Cone Forms. — Lathe Center, Fig. 8, B; Flat head Screw, Fig. lo; Countersunk head Rivet, Fig. lo; Pan 
head Rivet, Fig. lo; Blanks for Bevel Gears, Fig. i6; Reducing Coupling, Fig. ii, B; H,-L,-U, Fig. 44. 

Sphere Forms. — Ball Crank Handle, Table 6; Ball Lever Handle, Table 6; Button head Rivet, Fig. 10; 
Round head Screw, Fig. 10; Railing Fitting, Fig. 11, U; N, Fig. 44. 

Torus Forms. — ^Return Bends, Fig. 11, J, K; Elbows, Fig. 11, G, H, T, and X; T, Fig. 44. 

Miscellaneous Forms.— Machine Handle, Table 6; Latch Handle, Fig. 8, A. 



CHAPTER X 

ISOMETRIC DRAWINGS AND CABINET PROJECTIONS 




Fig. 46. 



259. In Fig. 6, C, is shown the pro- 
jection of a cube obtained by placing the 
cube so its dimensions of length, breadth 
and thickness make equal angles with the 
plane of projection. It does not other- 
wise differ from any ordinary projection. 
It is called an Isometric Projection. In 
Fig. 45 is shown such a projection of a 11" 
Cube. The edges in the projection will be 
less than 1\" because of fore-shortening. 
In the same figure, is a drawing similar to 
the projection, but larger. In this draw- 
ing, the lines representing the edges of the 
cube are just 1^" long. This is called an 
Isometric Drawing. It is a special form 
of an Axometric Drawing, and all the 



99 

principles and methods applicable to the latter apply to it. Its peculiarities are as follows. The axes of 
reference, BA, BG. and BC are 120° apart and a unit length on any one of them wiU measure the same as on 
any other. Thus the edges of the cube will all be of the same length in such a di'awing. One scale for 
measurement is therefore needed, instead of three as in axometric. The line BC is usually vertical and this 
makes AB and BG 30° Unes. EUipses for all three planes are also the same 
shape and similarly placed relative to the axis of reference. The major axis 
of the ellipse for each side face is inclined 60°. 

It is obvious that an Isometric Drawing is the simplest kind of an 
Axometric Drawing and tliat it is particularly adapted for instrumental 
construction. 

260. Referring to the Isometric Drawing of Fig. 45, two methods 
are shown for drawing the Isometric Ellipse. The one in the top face of 
the cube is an exact construction for the eight points used. These points 
are the middle points of the sides and the extremities of the major and 
minor axes. Point P is foimd from point L bj' the constiiiction indicated. 
LO is parallel to AB. 

In the right face is shown a method employing circular arcs with cen- 
ters at H, B, J and K. The method is approximate only, the error being 
indicated bj- the dotted arc with G as a center. 

The approximate ellipse should never be used as an intermediate 
construction for getting other figui'es. In the left face is shown a method 
for drawing irregular figures of any kind by plotting. 

261. In Fig. 42, K, is shown an isometric drawing of a hexagonal 
nut. See also, Section 189 for its constiniction. 

262. Isometric cross section paper is obtainable and affords a ver\- 
convenient way for making an isometric sketch. Such an one is shown in pjg. 46. 




100 



Fig. 46 with complete dimensions. No explanation is necessary, beyond saying that ellipses should be drawn 
before the side lines of the cylinders. Such a drawing can be easily scaled. It is half size. 

263. Exercises. For practice work on Isometric take the same drawings that are arranged for the 
Axometric exercises, Section 258. 

CABINET PROJECTIONS 

264. In Chapter I, it was explained that Cabinet Projection is a special kind of Oblique Projection 
obtained by placing the object and taking the projecting lines in a peculiar way. The typical form of this pro- 
jection is shown in Fig. 4, B. 

The customary way to make the drawing is to draw one face in its true size and shape. Lines perpen- 
dicular to this face are drawn at 45° and one-half their true length. 

A circle in the front face is therefore drawn as a circle, but in a side face it would be drawn as an ellipse. 

The method for the ellipse in the side face is shown in Fig. 4, A. The 
curve is drawn through the middle points of the sides of the circum- 
scribed square. Four other points are found on the diagonals from 
points a and b in the front face. 



Cab/net 

FfftK/eCT/OA/ 



■Scale. 
Half <Siz£ 




265. Fig. 47 shows a Cabinet Projection with complete 
dimensions. 

266. Oblique projections, similar to cabinet projections, arc 
often used in which the front face is shown in its true size and shape 
while edges perpendicular to this face are drawn at any convenient 
angle and made any convenient length not over full size. Fig. 7 is 
such a drawing. Edges perpendicular to the front face are 30° lines 

and their lengths are one-quarter size. 

267. Exercises. For practice work take the following. Fig. 48, A-B-C-H; Fig. 9, Gauge Stop, Hoist 
Arm Yoke; Fig. 44, B-D-J-P-V; Fig. 31, B-D-F. 



Fig. 47. 



101 

CHAPTER XI 

COMPARISON OF METHODS OF REPRESENTATION 

268. The different methods of representation are not equally adapted to all purposes. The following 
comparison maj^ not be agreed on by all draftsmen, but it is a fair statement. Isometric Projection is not con- 
sidered, as it is not used. An Isometric Drawing has all its advantages without its difficulty of scaling. 

GEOMETRIC PERSPECTIVE 

269. PictoriaUy, a drawmg of this kind may be very satisfactory if the visual angle is small. It has 
several imavoidable and objectionable distortions such as the tilting of the horizontal ellipse. It is not well 
adapted for rapid execution on account of necessary construction. Such a drawing should be made with instru- 
ments to secure a proper amount of accuracy. It is not adapted to dimensioning because of convergence of 
parallels. It cannot be used as a working drawmg, because it cannot be scaled and because of the confusion 
caused by hidden lines and fuU lines of the object. Though its underlymg principles are comparatively simple 
they are not quickly grasped. 

A da-awing of this kind is especially useful for architectural drawings of buildings and manufacturmg 
plants, and is sometimes the only way in which they can be represented. A photograph is a true perspective 
and less expensive, but in many confined situations, a photograph cannot be made. Fig. 2, A, is a Geometric 
Perspective Drawing. 

ARTISTS' PERSPECTIVE BASED ON AXOMETRIC 

270. PictoriaUy, this is the most satisfactory of all drawings. It has no distortions and is therefore 
pleasing to the eye. It can be made free-hand with great rapidity, but not so rapidly with instruments. It is 
not adapted for dimensions, nor for working drawings, because of the convergence of parallels and because every- 
thing is crowded mto one view. The principles on which it is based are simple and its methods are quickly 
acquired. 



102 

It is undoubtedly the best kind of a sketch for rapid and forcible free-hand illustration of the details of 
engineering construction. 

COMMON PROJECTIONS 

271. Pictorially, a drawing of this kind is apt to be deficient, because some study may be required in 
reading it. This will depend on the simplicity of the object. Hidden lines can be represented with less confusion 
than in any other kind of drawing. It has no distortions. It is adapted to rapid execution free-hand and still 
better adapted to instrumental drawing because of its verticals, horizontals and circles which predominate. 
On account of the possible multiplication of views its carrying capacity for dimensions and specifications exceeds 
that of any other drawing. Neither can the meaning of a dimension be misunderstood. Its principles are 
simple and quickly learned. 

It is above all the best drawing for mechanics and engineers to w'ork by. 

ISOMETRIC DRAWINGS 

272. Pictorially, this kind of a drawing lacks the distortions of a Geometric Perspective and possesses 
those due to lack of convergence. The available positions of the object are very limited. Overlapping of parts 
and coincidence of lines often makes it difficult to read. It is adapted to rapid execution especially with instru- 
ments and of all the drawings showing three dimensions, it is the best adapted for dimensioning. It is often 
used as a working drawing for simple parts. It is simple in theory, usually easily understood and applied. A 
drawing of this kind is used considerably for showing interiors of buildings and details of construction, as it can 
be quickly drawn with instruments. Fig. 6 A, is an Isometric drawing. It is better adapted for this illustra- 
tion than a Geometric Perspective, because convergence of the projection lines would give a wrong impression 
to a student. 

OBLIQUE PROJECTIONS 

273. A drawing of this kind possesses all the objectionable distortions of Geometric Perspective. Many 
draftsmen approve of it, because of its resemblance to Geometric Perspective, forgetting that its resemblance 



103 

is only of the worst features. More than this, it has the distortions of Axometric and Isometric, namely, lack 
of convergence of parallels. Its principle ^d^tue is that it can be quickly made free-hand or ■s\'ith instruments. 
It is not suitable for a working drawing as Fig. 47 wiU suggest. It should never be used for representing curved 
forms on account of the ^?iolent distortions. 

In spite of its deficiencies, it is often useful. Fig. 7 is an Oblique Projection and it is better adapted to 
the conditions than a Perspective or Axometric would have been. A Perspective would not have permitted 
parallel projection lines, but would have permitted bringing aU faces of the cube to a position showing their 
true shape. An Axometric would have satisfied the first condition, but not the second. A Cabinet Projection 
would have met both conditions satisfactorily, but would have caused bad overlapping of views. 

CABINET PROJECTIONS 

274. Cabinet Projections have all the deficiencies that can be imagined. The}'' have the bad distortions 
of Geometric Perspective, the distortions of Axometric, the limitations of position which Isometric has. Never 
use it for anything but rectangular fonns. Fig. 47 shows how poorly it is adapted for a working drawing. 

CHAPTER Xn 

SHADE LINES AND LINE SHADING 

275. If an object is illuminated bj' direct light it wiU cast a shadow. The outline of this shadow is com- 
posed of the shadows of certain edges or lines of the object. A line which is said to cast shadow is one which 
separates a lighted surface from one that is in shade. In a projection drawing, these lines are made twice as 
heavy as the other lines and are called shade lines. The object of using shade lines on a drawing is for the 
pictorial effect only. Thej' impart an appearance of solidity. Shade lines are now seldom used on working 
drawings, but are often used in drawings made for purposes of illustration. 

276. Light is assumed to be coming do-^Ti in parallel rays over the left shoulder of the observer as he 
stands looking at the object which is supposed to be built out solid on its projection. The slant of the rays 



,\ /-LAAf 



Use or Shade Unes 



\ i^ 



X Elevatjom 



\ 



E 


\ 


r 


\ 




\ 


G 


\ 


H 





V 




y 


x^ 


F 








\ 




/ 




\ 




N. 






/ 


\ 


















/ 






K 


/ 









: 

' ' ~ I 




\ E 






'mmmm 




o 


O 


o 




^ o 




o 


O 


o 




_ o 




o 


o 


mvET 


HOLES 


>)/VO HEADi. 







M 



I r o 



^^ 



Fig. 48. 



105 



is such that their projections on the planes of projection have an incUnation of 45°. To select the lines that cast 
or form the shadow, the pencil may be set up as a light ray, as shown in Fig. 48, P, and applied to the projection. 

In the square frame Fig. 48, A, the front surface is in the light while the surfaces at FH, GH, JK and JL 
perpendicular to the plane of the paper are in shade. 

The lines mentioned, therefore separate light from dark surfaces and will be made heavy. Note that the 
shade lines on the plan of the frame have been selected as if it were an elevation. In selecting shade lines, the 
view is always treated as if it were a front view. The various drawings in Fig. 48 fully illustrate present practice 
in use of shade lines. Shade lines for cylinders, cones and spheres are selected in a conventional way as indicated. 
Theoretically, the shading of a line should be on the outside of a projection, but such a rule cannot often be 
followed. It is more frequently put on the inside of the line of the projection. At K and M are drawings of 
connected parts which show how the shading is applied to avoid notching of the lines. 

277. If it is desired to carrj'- the pictorial effect still further, this can be done best by representing the 
light and shade effect on the surfaces. There are various ways of doing this, ranging 
from the complex productions of the artist to the conventional representations of the 
mechanical draftsman. The latter method only will be presented here, and very briefly 
too, as it auns to be suggestive merely. 

The positions of object and observer and the direction of the light are assumed 
the same as for shade lines. The general appearance of surfaces having various positions 
relative to the light and to the plane of projection is fully illustrated in the drawing of 
the hexagonal block shown in Fig. 49. The surface A-B is in the light and inclined to the 
plane of projection. The part nearest the observer appears the brightest and the change 
in shade from darkest to lightest is a uniform one. 

The effect is obtained by using a line of uniform width and increasing the space uniformly from back to 
front on the surface. If this increase of space width is not uniform, the surface will appear curved. 

The surface B-C is in the light and parallel to the plane of projection. The light appears uniform on the 
surface and the effect is obtained by using a line of uniform width and a space of uniform width. The bright- 




Fig. 49. 



106 



ness depends on the width of line and of space, but it is better to use a fine line than a wide space to secure 
a light effect. 

The surface C-D is in the shade and inclined to the plane of projection. The part nearest the observer 
appears the darkest and the change from dark to light is uniform. The effect is obtained by using a hea-\^ line of 
uniform width and by increasing the width of space uniformly, though slightly, between the front and back edges. 

Some draftsmen prefer to have surface B-C the same shade as the darkest part of A-B. In this case, 
A-B should be much lighter at B. 

278. In shading the preceding flat surfaces, a line of uniform width was used on 
each and the same method can be used in shading curved surfaces, particularly small ones. 
Better results can be obtained usually though by changing the width of both line and space. 
Consider first the convex vertical cylinder shown in Fig. 50. Referring to its plan 
showing the projections of light rays, it is seen that light striking an element H, 22^° 
to the left of the center, is reflected to the observer in a direction perpendicular to the 
plane of projection. R is therefore the brightest strip on the surface. The light is seen to 
be tangent to the surface at the element T, 45° to the right of the center. Element T 
will therefore be the darkest strip on the surface. These two lines at R and T divide 
the surface into three parts which will be considered separately. 

The portion A-B as in the case of the hexagonal block, will appear darkest at A, but the 
change from dark to light is abrupt near A and more gradual near B. To get the effect, start at A with a line 
of medium width and as B is approached let the line narrow very gradually, but widen the spaee more rapidly. 
The surface from B to C corresponds approximately to the same surface on the hexagonal block except 
that there is a gradual change at B to the brightest and at C to the darkest parts of the entire surface. To 
get the effect, increase the width of line and decrease the width of space very gradually in working from B to C. 
The part C-D is in the shade and inclined to the plane of projection, but also curved. It will be very 
slightly lighter at D than at C. To get the effect, narrow the line, at first gradually, then abruptly, in working 
from C to D and keep the space a narrow, uniform width the same as at C. 




Fig. 50. 



279. 




Fig. 51 




A hollow cylinder is shown in Fig. 51 and the method of locating the dark and Hght hnes. 
get the effect, shade the portion from A to B just like the 
part from C to B on the convex cylinder. Shade the portion 
from B to C just like the part from B to A on the convex 
cylinder. 

280. A shaded cone is shown in Fig. 52. The light 
effect is obtained in the same way as for the convex cylinder. 
As each line must taper from base to vertex, use a needle 
to rest the straight edge against at the vertex and set the 
pen to make a fine line. Each heavy line is composed of a 
series of fine ones. The beginner will get them too heavy 
unless he is careful. 



107 

To 



Fig. 53. 



281. The torus in Fig. 53 is shaded like a convex 
cylinder vertically and then horizontally. This gives the 
effect of double curvature. 




Fig. 52. 




Fig. 54. 



282. In Fig. 54 is shown a simple method of shading a spherical surface. It does not give a correct 
efTect, but the exact effect is obtained only by methods of lining which require much skill and time. 

283. A half torus or return bend is shown in Fig. 54, the effect being produced by setting the center of 
shading lines a little above the center of outlines. 



108 

CHAPTER XIII 

FREE-HAND LETTERING 

284. Although many styles of alphabets have been devised, only a few of them are adapted to rapid 
off-hand work or otherwise suitable for drawings used in construction. The novice is often confused in his selec- 
tion by the great wealth of available material, and it is partly for the purpose of avoiding this that a very lim- 
ited number of styles has been presented here. If one masters thoroughly the single stroke Gothic, he will have 
little difficulty with any other style. 

Any free-hand lettering looks well, if it conforms to certain fundamental principles which insure uni- 
formity in general appearance. For this reason the plainest letters, if well made, are often quite as effective 
as more ornate ones. While the general tendency is toward the use of the simpler forms, the decorative styles 
are also in frequent demand by the draftsman. These could not be satisfactorily included in such a brief treatment 
of the subject, but the treatises by Brown, Day and Strange provide all that could be desired along this line. 
A comparison of the contents of these books with the collections of alphabets formerly published for the use 
of draftsmen will afford considerable instruction in lettering as a fine art. To inlay the surface of a letter 
with mosaics and geometric designs or to drape it with biological rarities, does not make it beautiful. Asa 
thing for use, its form should be recognizable, but beside this it may have so graceful a shape that there is 
pleasure in looking at it. 

Good lettering on a poor drawing will not redeem the drawing, but a good drawing may have its appear- 
ance ruined by poor lettering. Poor lettering affects our estimate of a draftsman's ability in about the same way 
that illegible handwriting impresses us regarding the writer. Ability to letter well depends on the same qual- 
ities as free-hand drawing. It is needless therefore for a student to say he cannot letter well, that he has no 
talent, is no artist. For what he calls talent is merely the natural ability to observe correctly, combined with 
muscular control. Inasmuch as both these powers may be acquired without excessive exertion, he can learn free- 
hand lettering by a little expenditure of reason and will. 

285. Mechanical lettering differs from free-hand lettering in that the letters in their final forms are 
made with instruments although they may have been first sketched free-hand. The curved parts are lined first 



109 

by means of the compass or curved ruler, straight parts with the tee square and triangles. A combination of 
mechanical straight parts and free-hand curved parts is usually unsatisfactory unless the draftsman is an expert. 
Care regarding tangencies of straight lines and curves is as essential as in geometric drawing, so the process is 
apt to be a tedious one. This excessive amount of time devoted to a minor matter constitutes the chief objec- 
tion to the use of mechanical lettering on commercial drawings. From an artistic standpoint, a mechanical 
letter is often objectionable on account of its extreme precision and exact duplication, just as a piece of machine 
carving is less pleasing than that done by hand. With free-hand letters, this lack of flexibility does not exist 
because slight variations are unavoidable and no two As or Bs or Cs wiU be exactly alike. 

286. A^TiUe mechanical or free-hand letters may be weU formed and satisfactory as letters yet they may 
not harmonize with their smroundings. Imagine the appearance of Old English type on a working drawing, 
or, if you will, the plain modern Gothic entwined with the traceries of a ]\Ioorish archway. The primarv^ object 
of words is to say something. If the statement be in the form of a notice, the simpler the expression and the 
plainer the letters the better. If, however, we have a scriptural quotation used to fill bare space on a church 
wall, then something ornamental is desirable. Thus the question of lettering quickly merges into one of deco- 
rative design and the simpler forms of letters wiU be found modified into unusual shapes more or less artistic 
as wiU be seen by reference to memorial tablets, book covers and magazine advertisements. 

287. Students (generally poor letterers) wiU often say, ""VMiy should a draftsman leam to letter weU; 
don't most drafting offices employ boys to do such work? " Their idea is, of course, that in the development 
of the division of labor in the drafting office, the first man makes a sketch of the design of a machine, a second 
man elaborates details in pencil, a third makes a tracing of these in ink, a fourth puts on dimensions and a fifth 
the lettering. This may be aU right in theory and it is in part the practice in some large establishments. In 
the great majority of cases, however, it wiU be found that the draftsman who begins the drawing does aU the 
work on it. The only printing he may sometimes avoid is that for the title. In this matter practice varies, 
but the end in view is to secure uniformity and to economise time. It is for this reason that a boy who has 
a natural knack at lettering is often employed at low wages to put in all general and sometimes the sub-titles. 
The general title is often printed on a press with blank spaces to be filled in ; or it is printed with rubber type 



110 

and lined over to make the letters opaque for blue printing; or the title is traced from a copy placed underneath. 
The dimension figures and printed specifications are put on by the draftsman who knows the drawing. And 
these dimension figures especially must be so definite in form and prominent in size that they are not easily 
obliterated even in the blueprint. Too much care cannot be exercised in this particular, for a slight irregularity 
in the drawing may cost hundreds of dollars to rectify when it has been duplicated in hard metal. A beam too 
short or a bearing out of place is an error not easily corrected and the responsible draftsman will pass through 
an uncomfortable season. 

FUNDAMENTAL PRINCIPLES 

288. Height and Width of Letters. The underlying characteristic of good lettering is uniformity in 
general appearance. This applies to the height and width or to the apparent area covered by the individual 
letter. Referring to Fig. 55, hnes 1 and 4, we see that all the capital letters are of the same height and nearly 
all have the same width which we may style the normal width. The exceptions are the I, the J which is roughly 
I, the M which is |- and the W which is ^ of the normal width. Figures are about I- of normal width. Looking 
at the small or lower case letters of this alphabet we see in line 7 that the heights are variable. There is, first 
of all, a body in nearly all the letters, of a height equal to -| that of the capitals. Six of the letters, b d f h k 1, 
rise above the body to the full height of capitals, while a seventh, t, falls a little short of this height. Five of 
the letters, g j p q y, have parts extending below the body as far as the stems of the other letters extend above. The 
remaining letters aceimnoisuvwxz have only the body, if we except the i which has a dot. The normal width 
of the small letters is about | of that of capitals. The f i j 1 r t are narrower, while the m and w are greater than 
normal width. The ratio of normal width to height for capitals and the bodies of small letters should be about 4- 

289. While the uniform heights and widths of letters as shown in the plates are satisfactory for the 
ordinary small sizes, they will often need modification in the larger ones in order to secure uniformity in apparent 
size. For instance, if the letters A B R S are all of the same width, the A will appear narrower than the B 
and the S than the R.. When such is the case, the letter which seems narrow should be widened enough to over- 
come its defect. In the same way the C G and Q may appear a little too short especially when placed to the 
left of a letter hke the B or E. 







yirijrr^Uii ./,'^ 



i- ~? 



\ 



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..fiCm & J LWlWM?fi 



- v^.iii\/wxM:/ i^-'^-mi.iim^w 



sSVUVWX YI fPS^SB 7890 

^ S UVW Yi ^' '& &P0 

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s ABCDEFEHIJKLMNnPPRSTU 
'0 VWXYZL Fan TiTLEB I234SE7B3D 

Fig. 55. 



112 

290. If lower case letters are being used, the common rules relating to use of capitals should be followed. 
Words requiring Emphasis maj- be Capitalized, either on the Initial or THROUGHOUT. If capitals only are 
used THEY MAY BE ALL OF THE SAME HEIGHT or Initials may be Larger on the Prominent 
Words. A word of minor importance like the "of" Fig, 6i, Title 1, line 2, would not have an enlarged initial 
unless it stood first in the line like "The" in the fourth Une of the same title. When large and small capitals 
are thus used, the small ones should be about f the height of the large ones. As they have no parts 
extending below the base line, capitals permit the use of a larger letter for a given vertical space than 
is possible where lower case letters are used. This is frequently of importance when condensing material in 
a table. 

291 . When letters and spaces are narrowed to less than normal width as compared with their height, they 
are said to be COMPRESSED; when they are made greater than normal width, they are said to be EXT EN D ED 
Extended lettering will often look better than the normal as errors in parallelism are not so noticeable. The 
printer specifies a letter height by points. These range from 5J to 72 points in metal sizes and a limited range 
of these is shown in Fig. 60. 

292. Slant of Letters. Uniformity in the slant of letters is essential. Letters may be vertical as in 
"Worcester," may slant forward like common handwriting as in "Polytechnic" or backward as in "Institute." 

See Fig. 56. The vertical form is the most difficult as even an untrained eye 

\A/r) O ^ p" O ~r p" D notes slight variations from the erect position. The forward slant is most used, 

v-/ L_ vJ l_ I especially for rapid work. The inclination is about 22° from the vertical or a 

ZZX-j/ \y Y' F~ r^ l-l l\l I r^ ^'^^^ of 5 on a base of 2. See Fig. 55, line 4. A beginner will sometimes do 

' ^'— ' I L—K^niylly^ better with the back slant than with either of the others. It should always 

\k\ o-r-x-r-\ \-r r" be tried, especially if the writer is left-handed. 

'^^'^^^^^^ *— It is customary to draw the top and bottom limiting lines for lettering 

^'s- 5®- of any kind. The slant of letters is determined by reference to these lines 

whether they be straight or curved. For instance, the limit lines for "Map of" on Fig. 61, Title 2, are arcs of 

concentric circles. In map drawings it is often necessary to use irregular curved limit lines as in "Salisbury St., " 



113 




T:^sx. 



Fig. 57. 



Fig. 57. Note that the parts of the letter which lie on the limit hnes in straight lettering are found coinciding 

with the limit lines in curved lettering. In the same way the slant of any 
particular letter will be determined by the direction of the curve at its position. 
Sometimes, however, in ornamental work, vertical letters are used, as in 

"BOYNTON," Fig. 57. 

293. styles of Letters. There should be uniformity in the style of 
letters employed for the same body of text and usually for the entire drawing. 
Variation in styles is permissible in titles or for purposes of classification. As to 
the latter, in case of maps for instance, state names might be in one style, 
cities and towns in another. The tendency, however, is toward uniformity 
even here, with variation in the size or slant only for different features. 

294. A common error is the mixture of capitals and small letters indisciiminately thus, Drop ForoinGs; 
or the mixture of Roman and Gothic, thus LATHE. 

295. Spacing of Letters and Words. We must have uniformity in the apparent spaces between letters 
and the actual spaces between words. For small letters not exceeding j" high, in which the upright part is 
formed with a single penstroke, the normal space width may be J or ^ of the normal letter width. That a defi- 
nite rule generally applicable cannot be formulated is shown by the word "SMELTER," Fig. 58, upper line, in 
which the spaces between letters are all equal. On account of the large area 
between the L and T, the word appears to be broken in two parts. If this 
space is reduced enough to give the appearance of uniform spacing, as in the 
second line, we find that the T actually overhangs the L. The same modifica- 
tion of spacing will be necessary with the various combinations of A C F J L 
P Q T V W and Y which, it wiU be noted, are the letters that do not fill out 
their parallelograms. Space letters so they appear to be evenly distributed 
throughout the word. If we drop a letter out of a word thus, Labo atory, the space between the and A is the 



SMELTER 
SMELTER 



Fig. 58. 



114 

requisite amount for readable spacing of words. A good phrase to remember is, "Crowd letters ; spread words." 
It is natural to do the reverse. If, as sometimes happens, it is impossible to provide a proper amount of space, 
the division into words may be effected by using a large capital initial for each word. Extra space must be 
allowed for punctuation marks between letters or words. Title 3, Fig. 6i, shows an exception to rules for spacing. 

DESCRIPTION OF ALPHABETS 

296. Two alphabet styles, the Roman, Fig. 59, lines 1 and 2, and the single stroke inclined Gothic, 
Fig. 55 lines 1, 4 and 7, are used more than any others for drawings pertaining to engineering. The Roman 
is used especially in topographical work and the single stroke Gothic for shop drawings. This sentence is printed 
in Gothic. The word "Simple," Fig. 59, line 11, is in Outline Gothic. In the same way we have Outline Roman 
and Inclined Roman or Italic. The alphabet given in Fig. 59, lines 3 and 4, is a modification of the latter suitable 
for single stroke work. A single stroke Gothic capital may be changed to the Roman by the addition of serifs, 
the short horizontal terminals; kerns, the short terminals projecting from one side of the line and by increasing 
the line width on certain parts thus, A to A, E to E. The Roman is a more elaborate letter than the Gothic, 
requires more time to make and is therefore less suitable for rapid work. The single stroke inclined Gothic 
being the one most easily understood and acquired is the style best adapted for the beginner's first attempt. 
It illustrates all the cardinal principles of good lettering and it is but a step from this to the Roman, thence 
to other more elaborate forms. See an analysis of it in detail under the topic, "Directions for Practice Work." 

The letters shown in Fig. 55, lines 9 and 10, are adapted to either free-hand or mechanical construction, 
but especially the latter as there are no curved parts. Lower case letters of the same style may be used, but 
they are not satisfactory from the standpoint of appearance and economy of time. Note that the heavy shad- 
ing is on the top and bottom horizontals only. 

In lines 1 and 2, Fig. 59, we have the vertical Roman. These letters must be formed with considerable 
care if they are to be presentable. Lack of parallelism, either in the general outlines or in the edges of shaded 
parts detracts much. The serifs too, must curve very nicely into the parts they terminate. If they are tilted, 
the result is markedly offensive. The letters in lines 3 and 4, Fig. 59, have already been referred to as modifi- 
cations of the Roman letter suited to off-hand work. 



/ ABCDEFGHIJKLMNOP0RSTUVWXYZ& 

2 abcdefghijklmnopqrstuvwxjz 123456789 

J ABCDEFGHIJKLMNOP0RSTUVWXYZ& 

4 abcdefqhijklmnopqr&tuvwxi/z 125456789 

s ABCDEFGHUKLnNOPQRSTVVWXYZ 
6 LOOKS-BEST^COnPRESSED ^ - 123456789 

^A^^OErretiimLn/IOPQRSTUVWXYZ 

5 avlo<?deFgr2iikln2i2opG|r6havwxyz 12(3. 4- 5 6 789 

9 7ID6peT(^?ilJM;ANO?ail5Ti/\^WATZ 

//SiyPLE yETHODS sujtaslf: f 



Fig. 59. 



116 

While most styles of letters look well in the vertical, forward or back slant position, those shown in lines 5 to 
10, Fig. 59, are satisfactory only when vertical. They are free in style, easily made and, as such, well adapted 
to architectural drawings. Those shown in line 5 look best compressed. Of the three, that given in lines 7 and 
8 permits most rapid work. 

In lines 11 and 12, Fig. 59, are indicated some of the possibilities in the way of adorning so plain a letter 
as the Gothic. The simpler the treatment the more pleasing the result. Many other modifications will suggest 
themselves and for those who lack originality, a look through the magazine advertisers may afford inspiration. 

297. Old English, Fig. 60, is used chiefly for engrossing diplomas, certificates of membership and sim- 
ilar documents. Round Writing, not given here, has been used to some extent for working drawings, but though 
it can be rapidly made, looks well and is easily learned, its lack of legibility has prevented its general adoption. 

TITLES 

298. General Character. A general title contains the principal information necessary to identify 
the drawing with the matter represented. Its location will vary according to the character of the 
drawing, being most frequently in the lower right hand corner. The size of title space depends on the size of 
sheet, those given in Fig. 61 being appropriate for sheets up to 18" x 24" in size. For a sheet 24" x 36", the 
title and letter dimensions could be increased 50% or more. The shape of title space is determined by the kind 
of drawing and the contents of the title, but it is usually rectangular with the long dimension horizontal. Its 
arrangement will be symmetrical with respect to a vertical center line. Vertical letters produce the best effect 
in a title and a mixture of vertical and inclined letters is not satisfactory. The size of letters and spaces between 
lines should be so selected that the title will appear well balanced or distributed over the space. The several 
parts of the title may be lettered to correspond to their importance, proper prominence being obtained by judi- 
cious use of different sizes and styles. See Fig. 61, titles 1 and 2. Let the style of letters be appropriate to the 
character of the drawing; the fewer the styles in one title the better. 

299. Titles for Working Drawings. The title for a working drawing will specify the name of the machine 
or structure represented and generally the groups of parts to which the sheet is devoted. If the machine or struc- 




alcbcffllijliliiiuo}) iirst 
u b to f u 5I 2 3 i d 6 7 8 fl 




- 2 



6 Point 

8 Point 
10 Point 

12 Point 



14 Point 

18 Point 

24 Point 



30 Point 

36 Point 



Fig. 60. 



118 

ture is for some special use or location, it is often so stated. To this is added the name and location of the 
makers, the scale and date of the drawing, with the name or initials of the draftsman who made it. In many 
titles, spaces are left for the signature, by initials only, of those who trace, check and approve the drawing. 
Occasionally we find the name of the designer attached. The job or order number is also often placed in the 
title. Title 1 of Fig. 6i is a form suitable for working drawings. Titles for this class of drawings are almost invari- 
ably placed in the lower right hand corner close up to the border. They can then be referred to conveniently 
when filed in a drawer with many others. Every drafting office has its own standard title form and this is 
of such shape and size as will meet its special needs. Though fanciful lettering is sometimes found on commercial 
drawings, the general tendency is toward extreme simplicity. The plain Gothic, either heavy face or single 
stroke, is the prevalent style employed and the largest letters will rarely exceed ■^" in height. 

300. Map Titles. The title of a map or plan specifies the locality represented, the scale and date of 
the drawing, name of the draftsman and usually the name of the surveyor or engineer. If the drawing has been 
made for a public commission or corporation, it is customary to include the name. The location, size and shape 
of the title will be determined by the available space outside of or even on the map. A uniform arrangement 
for a series is not generally possible unless a one or two line title is used. Roman and Gothic letters, plain or 
simply modified, are the ones commonly used, but it is quite permissible to arrange them to produce an orna- 
mental effect. Title 2, Fig. 61, will iUustrate this. It also shows how to grade the prominence of different 
parts of the title. For instance, "The World" if in solid black would give too heavy, while if in outline only 
it would give too light an effect. As the most important part of the title it has larger letters. 

301. Architectural Titles. Titles for architectural drawings follow no rule, but are treated with great 
freedom. In the majority of cases, such a title will designate "what" and "where" regarding the matter repre- 
sented, also the scale of the drawing. It may or may not have the date, name of the architect, draftsman or 
other useful information. Its location is as variable as its contents and it is liable to be placed anywhere, 
even on the face of the drawing if such an arrangement is feasible. The size is usually such as to make it incon- 
spicuous. In fact, it is often made to resemble a formal title as little as possible. As to shape, the rectan- 
gular is most common and the long dimension will frequently be vertical, especially if the style be that shown in 









I 













8 



5: 



o 














"^1 



^ (5 ^^ 




Fig. 61. 



^ 



120 

title 3, Fig. 6i. In this form the rectangle is to be filled as completely as possible without reference to punctu- 
ation or the division and spacing of words. Outline Roman, Old Roman and the styles shown in lines 5 to 8, 
Fig. 59, are the ones most used. 

302. Laying out Titles. To locate symmetrically a line of letters in a title gives beginners some trouble. 
If the letters are pencilled first, they can be located by trial, but this is apt to be a tedious process if the 
line be a long one or the letters other than the simplest. Consider for example in title 2, Fig. 61, the line, 

12 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 

ON mercator's projection. Numbering from the left and counting a space between words as 
equivalent to a letter there are seen to be 23 letters and spaces. If letter widths were all normal, number 12, the 
S in Mercator's would be at the middle of the line. But as there is a wide letter, number 4, and a wide space 
for the apostrophe at the left of the S, while at the right are two narrow letters, numbers 17 and 21, it is 
necessary to shift the center of the line a little to the left of the S. Starting then with the S properly placed, 
work both ways from the center. If appearances indicate that the end letters are not coming just right, a 
slight modification in letter and space widths will overcome the error as the work proceeds. It will be easier 
for some to first mark off in pencil the space allotted to each letter. On account of the diflficulty of proper placing, 
it is advisable for beginners to pencil titles before inking, until the eye is sufficiently trained to dispense with it. 

DIRECTIONS FOR PRACTICE WORK 

303. Smooth, hard surface paper is the best for lettering as it helps insure a clean cut line and smooth 
working of the pen. This is quite desirable when lettering for reproduction. When tracing cloth is used, the 
surface must be thoroughly rubbed with powdered chalk or pumice and all particles removed before the ink is 
applied. 

304. A fine pen like a Gillott Lithographic is best for Roman letters and others having fine lines and 
shaded parts. For single stroke Gothic, a medium fine pen that has been somewhat used or a fine ball point 
pen will work well. The prudent draftsman will take good care of his lettering pen, using it for no other pur- 
pose. Its hould be cleaned frequently, as ink particles collect and dry between the nibs, spreading them so as 
to render the pen useless. Water-proof black ink is most used. 




121 

305. The upper and lower gtiide lines are always pencilled and to save time in practice, cross-section 
paper ruled in tenths of an inch may be used. Slant lines in pencil showing the 
inclination may be iiiled in intervals aU over the sheet. A rise of 5 on a base 
of 2 is a verj' good inclination to use. Tack the sheet on the board in such a way 
that the elbow is supported when at work, otherwise the motion wUl be cramped. ^^ X~ / ^ "^ Z' "j (^ " 

306. Practice first the strokes shown in Fig. 62, taking them in order. %^ vx L^ ^ I k/ ^^—^ 
They wUl assist in acquiring the necessarj- swing. Blackboard practice on these ^'s- 62. 

is ven,^ beneficial. It is needless to say, that at first, the mind must be concentrated on the pen point from 
the start to the completion of a stroke. After considerable practice, it wiU be possible to letter automatically 
just as we write, but until that time it is well to remember that lettering is a mind as weU as a hand exercise. 

307. Turning now to the alphabet of capitals in Fig. 55, lines 1 to 6, make two or three copies of each 
letter and figm-e. Before making a letter, note carefully in each case its general shape and proportions. The 
horizontal lines and enclosing parallelograms wiU assist in this. The parallelograms should always be sketched 
in pencil if the letter gives trouble as is generally the case with those having oblique parts like A, K, etc. 

308. Next study the sequence of strokes as shown in lines 2, 3, 5 and 6. T^^lere two methods are given 
the first is desirable for rapid work, but if the beginner does not master it at once, let him try the second. Other 
ways than those given may be used if they produce good results. After going through the capitals in this fashion, 
look over the work critically, mark the letters with which you have had the least success and devote extra prac- 
tice to them. It may be said here that the enjoyable way to learn to letter is not to practice half a day at a 
time once a month, but rather to spend a quarter-hour each da^'. Practice on the letters by groups is also desir- 
able. Thus the A K M N V W X Y Z may be classed as the ones with predominating oblique parts, the B D E F 
H L P R T as the ones with horizontal parts, while C, G, and Q belong to the ovals, leaving the I, J and S 
as miscellaneous. Attention has been directed to the I, J, M and W as letters of abnormal width. Other pecuh- 
arities should be noticed as follows. The mid-horizontal parts of the A and G and the intersection point in the 
Y are the same height, a little below the middle. The corresponding parts in the B E F H R and X are slightly 



122 

above the middle while in the P it is at the middle. The upper lobe in the B and the S is slightly smaller than 
the lower one. Invert the letters to see it plainly. The lower oblique part of the K if extended will intersect 
the top end of the upright part. The M and W must be carefully distinguished as it is a common error for a 
student to make an M like an inverted W, and vice versa. Among the figures, the upper part in the 3 and 8 
is smaller than the lower. The 9 is the 6 inverted and the general outline of each coincides with that of the zero. 

309. Lower case letters are to be practiced in the same way as the capitals. Those of abnormal width, 
the f i j 1 m r t and w, have already been mentioned. In the abcdegopq are ovals and straight parts, in 
the f h j m and n are hooks and straight parts while the u v w x and z are like their capitals. Note that the 
cross-piece for the f and t is on a level with the tops of the short letters and that the upper oblique part of the 
k terminates at the same height. 

310. When an ink line is led out of another not dry and the angle is small, a blot may form at the notch 

as is indicated in Fig. 63. Such blotting as shown in the word "pen" may be 

jT^^ri i ItDj^^^ll^jh avoided by carrying less ink on the pen or by breaking up the stroke as is 

I / "^ ^ shown in the second part of the same figure. The principle is to lead into, but 

not out of a wet line. This blotting is less liable in the Eeinhardt letter than in 
'^'^- ^^- the single stroke Gothic. 

311. If the beginner has no immediate success with letters of nonnal width, let him try the extended 
form, making his width equal to or greater than the height. 

312. The prominence of poor lettering may sometimes be reduced by heavy underlining. 

313. Practice lettering in pencil is not advisable when ink is at hand as it permits thoughtless work 
on account of being so easily corrected. 

314. It isuseless to attempt free-hand lettering with chilled hands or immediately after severe muscular 
exertion. 



123 
LETTERING FOR PHOTO REPRODUCTION 

315. A drawing may be reduced even to microscopic size by photography, but the chemical and mechan- 
ical manipulation necessan- in producing the metal plate used for printing imposes some limits. For many draw- 
ings, it is desirable to have the final print smaller than the original because the imavoidable irregularities of 
free-hand work are thereby reduced in prominence. Some ch-aftsmen, however, prefer little or no reduction 
because the effect of the original may be materially changed. The amount of reduction possible is really decided 
by the ^\-idth of the finest lines, as beyond a certain point they "^-iU become broken in the plate. A reduction 
to J or J the linear dimensions of the original is a good one. suitable for the width of medium weight pen strokes. 
Fig. 61 is of the same size as the original. Figs. 55 and 59 are i the hnear dimensions of the original whUe the 

cuts in the text of this chapter are -|. a reduction to a size less than that of six point type used in this sentence will generally be unsatisfactory 

on the score of legibility-. For the Same rcasou the spacing for veiy small letters should be more open. Notches and small 

loops have a tendency to fiU when the letters are smaU and it was to avoid this that the Reinhardt letter ^vas 

evolved and is used on its cuts by the "Engineering News." It is only a shght 

modification of the single stroke Gothic and aU the letters which differ materially /" // I 

are sho-mi in Fig. 64. The principal variation is in the slant of the ovals which [_J7 (7J f^ ^ (^ /O /^ 

is about 4.5° as indicated, while in the Gothic letter the corresponding slant \^' ^ / j 

would be about 60°. Compare with line 7, Fig. 55. Another variation is in the 1 ^ '^ ~7 /^ /^ 

hooks of letters such as the h, m and n where the hook is made more pointed /o /oo /o /-^, ) r^ ^ 

and leads from the straight stem at a greater angle. Loops are also exaggerated ' ' ' ' ' ' ' '■ — ^^ ^-^ — ^ 

as in the e. The upper and lower parts of the 2, 3, 6 and 9 are more nearly Fig. m. 

the same size. 

316. Waterproof black ink is the best to use for reduction work as there is no clanger of blurring it by 
accidental moistening. AU ink lines must be jet black, never grayish. Red coloring matter is sometimes put 
in the ink to insure its photographing properly. For the same photographic reason the paper used should be 
of a bluish rather than of a yellowish tinge. 



124 

ALTERATIONS 

317. Often a letter or part of one must be removed. The use of an ink eraser ig apt to demolish parts 
of neighboring letters, but it will leave a better surface for re-inking than will a sharp knife. It is best to pencil 
what is to be replaced and then use very little ink on the pen, otherwise the lines may have frayed edges. If 
a small part is to be removed, a sharp knife will be most satisfactory. First cut lightly the surface of the paper 
at the boundary of the erasure, being careful not to cut through. Then scrape carefully up to the edge of this 
cut and you will leave a sharp clean edge on the ink line. If the surface is such as would be spoiled by erasure, 
the parts can be painted over with " Chinese white" and ink applied on this. 

BOOKS ON LETTERING 

318. Text Books for Students 

Lettering for Draftsmen. C. W. Reinhardt. Text 32 pages. 9 Plates. D. Van Nostrand Co. 

The Theory and Practice of Lettering. C. E. Sherman. Text 49 pages. 10 Plates. Midland Publishing Co. 
/^ Free-hand Lettering. V. T. Wilson. Text 95 pages. 23 Plates. John Wiley & Sons. 

Text-Book on Plain Lettering. H. S. Jacoby. Text 82 pages. 48 Plates. The Engineering News Publishing Co. 

Free-Hand Lettering. F. T. Daniels. Text 34 pages. 13 Plates. D. C. Heath & Co. 
Collections of Alphabets suitable for engravers, jewelers, stone-cutters and sign writers. Chiefly mechanical 
in character. 

A Set of Alphabets. Copley. 47 Plates. 

Standard Alphabets. Prang. 34 Plates. 

Examples of Modern Alphabets. Delamotte. 48 Plates. 

Draughtsman's Alphabets. Esser. 21 Alphabets. 
Lettering as a Decorative Art 

Letters and Lettering. F. C. Brown. Text 214 pages. 211 Ulust. Bates & Guild Co. 

Alphabets. E. F. Strange. Text 294 pages. 197 illust. Geo. Bell & Sons. 
Contains also a good list of references. 

Alphabets Old and New. L. F. Day. Text 39 pages. 178 illust. Charles Scribner's Sons. 



23 
ff4 



29 

5-4 



Decimal Equivalents 
of Common Fractions 



1 



1 

^5 



3 



1 
T6 



/? 



3 



7 
5^4 



«4 



/j 



1 1 



1 3 



3 



7 
3^ 



I 5 



1 7 



9 



1 
54 



2 1 



5 



1 1 



2 5 
5^5 



27 



13 
5^ 



7 
TF 



] 5 



^1 



015625 


tf 




03125 




¥^ 


046875 


3 5 




0625 




A 


078125 


u 




09375 




*l 


109375 


u 




125 




t 


140625 


n 




15625 




¥r 


171875 


If 




1875 




1 \ 

Tff 


203125 


u 




21875 




?! 


234375 


H 




25 




f 


265625 


n 




28125 




M 


296875 


«i 




3125 




l# 


328125 


II 




34375 




U 


359375 


H 




375 




* 


390625 


S7 




40625 




fl 


421875 


H 




4375 




If 


453125 


U 




46875 




t* 


484375 


U 




5 







.515625 

.53125 

.546875 

.5625 

.578125 

.59375 

.609375 

.625 

.640625 

.65625 

.671875 

.6875 

.703125 

.71875 

.734375 

.75 

.765625 

.78125 

.796875 

.8125 

.828125 

.84375 

.859375 

.875 

.890625 

.90625 

.921875 

.9375 

.953125 

.96875 

.984375 



Whitney KErs 



Wood/jliff!s Sr^sTEM 




-M- 



C- Cutter Diam. 



No. C W P S L No. C W P S L 



1 


\ 


tV 


1 


A 


i 


2 


\ 


tt\ 


5^4 


A 


i 


3 


\ 


i 


A 


3 

FT 


i 


4 


f 


^\ 


3 

714 


1 
TF 


f 


5 


t 


A 


iV 


A 


f 


6 


t 


s 
1T2 


^4 


,V 


§ 


7 


f 


i 


,V 


.V 


f 


8 


f 


A 


^4 


A 


f 


9 


^ 


3 


3 


1 


3 


4 


Id 


3 2 


1 6 


4 


10 


I 


A 


^4 


A 


i 


11 


I 


A 


A 


1 


i 


12 


I 


7 

^2 


r 


I 
IF 


^ 


A 


i 


i 


i 


A 


i 


13 


1 


A 


A 


1 

TF 


1 


14 


1 


7 

1T^ 


7 


1 

TF 


1 


15 


1 


i 


* 


t'f 


1 


B 


1 


A 


A 


iV 


1 


16 


H 


A 


A 


F^4 


1* 


17 


H 


bV 


^V 


f\ 


1* 


18 


H 


i 


i 


f\ 


H 


C 


H 


A 


A 


F^T 


H 


19 


H 


A 


A 


F^ 


H 


20 


H 


ttV 


^4 


f\ 


H 


21 


H 


i 


i 


A 


H 


D 


H 


A 


A 


f\ 


H 


K 


H 


f 


3 

1 (T 


FT 


H 



22 


If 


i 


* 


A 


If 


23 


If 


T% 


A 


A 


If 


F 


If 


f 


r\ 


A 


If 


24 


n 


i 


* 


/t 


H 


25 


n 


A 


3\ 


7 

FT 


H 


G 


H 


f 


T^F 


7 
FT 


H 



No. C W P S M 



123 

111 

Iff 
1 23 

-^3 2" 

2A 
2A 
2A 
2A 

2 5 

-'TF 

2| 
2^ 
2i 
2f 
2f 
2^ 
2f 



26 


2* 


t\ 


A 


H 


27 


2* 


i 


* 


i^ 


28 


2i 


t'f 


A 


H 


29 


H 




T^F 


U 


R 


2f 


1 


i 


s 


S 


2f 


t% 


A 


# 


T 


2| 


f 


A 


t 


U 


2f 


tV 


7 


t 


V 


2i 


i 


i 


^ 


30 


3^ 


t 


A 


II 


31 


Bi 


7 

TF 


7 
1T2 


u 


32 


3i 


1^ 


i 


u 


33 


3i 


T% 


A 


II 


34 


H 


t 


A 


It 


35 


H 


U 


U 


M 


36 


H 


t 


f 


1 3 

TF 



US. Standard Bolts and Nuts 



H- 



"T" 
1 




A -Arta af/foof of Thread 
T-Diam. of 7a/> Dr/// 
DifTienifOns for 2q. ancf Hex are ^same i/^/esi fioted 



Dia. Thd. B 



i 


20 


^^ 


18 


f 


16 


tV 


14 


\ 


13 


T«F 


12 



li 
If 
li 
If 

2 

21 
2i 
2f 



11 

10 
9 



7 
7 
6 
6 
5 

4* 

4* 
4 
4 
3.^ 



3 7 

FT 
1 1 
TF 

5 1 

FT 

2_9 
'3 2 

Vt 



li 
IH- 

12 9 
-^'G 4 

Ifl 

If 



2 3 

2 « 

^TF 

2ii 
2f 

^TF 



93 9 

"^FT 

4-3- 
^6 4 

431 
^F4 
4.29 

5i-i 



2 3 

'3' 2 
27 
B^ 

ai 

3^ 

IfV 
li 



If 

IM 
3A 

2il 



2 9 

9B3 

''ft 

3 3 

92 3 

^FT 

^FT 



42 7 
*FT 
46 1 
^FT 

H\ 
6A 

6H 



1 9 

"3 2 

1 1 

1 S" 

2 5 



3 1 

B2 

lA 

U 

1t\ 

If 



1 1 3 

^TF 

2 

2A 

2f 

2| 



3i 
3* 
3f 
41 

4t 



1 .') 

FT 



I 9 

FT 

*-3 
F4 

1 % 

^2" 



1 S 
"52 

F4 



T_7 
F4 
2 7 



61 
FT 

1/t 
IH 

^FT 

1#^ 
-^F4 



Iff 

IH 

2A 

2 7 

"^TF 
On 

"FT 



.0260 
.0452 
.0677 
.0932 
.1257 

.1620 
.2018 
.3020 
.4194 
.5509 

.6930 
.8890 
1.054 
1.293 
1.744 

2.30 

3.021 

3.714 

4.618 

5.427 



125 



Table No. 1. 



Machine ScHEWS A.SME. Stand. Mach. and Wood Screw Gage 




Qy/iL FiLL/^TCR Head 

A-Diam. ^j! t V- 

B=I.6^A-009 

C^OMA-OOZ 

D^.I73A+.0I5 

E=./34B+C 

Flat Fillister Head 

\< B 

A = Diam. 

B- IMA- 009 
C^OMA-.OOZ 
D-0.I75A+.0I5 

El AT Head 



— Llrt 



T 



-A^ 



A=D;«m. y<^f! 
B=2A-008\\ H ^^ 

r- A -.008 y^ ■ 

^ /.739 E 

D=.l73Ai-.OI5 
Round Head 




A = Dia)^- 

B=l.85A-005 

C-0.7A 

D^J73Ai-.0/5 

E--2C+.OI 






-A> 










2 



5 



8 



10 



12 



14 



16 



18 



20 



ZZ 



24 



26 



28 



30 






.060 



.073 



.086 



.039 



.112 



.125 



.138 



.151 



.164 



.177 



.190 



.216 



.242 



.268 



.294 



.320 



.346 



.372 



.398 



.424 



.450 



80 



72 



64 



56 



4S 



44 



40 



36 



36 



32 



30 



28 



24 



22 



20 



20 



18 



16 



16 



14 



14 



-si 

I 



^'^ 



.04-65 



.0595 



.0700 



.0785 



.0890 



.0995 



.1100 



.1200 



.1360 



.1405 



.1520 



.1730 



.1935 



.2130 



.2340 
.2610 



.2810 



.2968 



.3230 



.3390 



.3680 



T.A.S.M.E. V0L.Z3P39 



No. 


D/AM. 


No. 


DiAM. 


000 


.03/52 


25 


.38684 


00 


.04468 


26 


.40000 





.057S4 


27 


.41316 


1 


.07/00 


28 


.42652 


2 


.08416 


29 


.43948 


5 


.09732 


30 


.45264 


4- 


.1/048 


31 


.46580 


5 


./2364 


32 


.47896 


6 


./3680 


33 


.49212 


7 


./4996 


34 


.50528 


8 


./63/2 


35 


.51844' 


9 


./762d 


36 


.53160 


JO 


.18944 


37 


.54476 


II 


.20260 


38 


.55792 


12 


.21576 


39 


.57108 


13 


.22892 


40 


.58424 


14 


.24208 


4-1 


.59740 


15 


.25524 


42 


.61056 


16 


.26840 


4-3 


.62372 


17 


.28156 


4A 


.63688 


18 


.29472 


45 


.65004 


19 


.30788 


4-6 


.66320 


20 


.32104 


4-7 


.67636 


21 


.33420 


4-8 


.68952 


22 


.34736 


49 


.70268 


25 


.36052 


50 


.7/584 


24 


.37368 







Twist Drill and St.I/I/irb Gage 


No. 


D/AM. 


No 


DiAM. 


No 


DiAM. 


1 


.2280 


28 


.14-05 


55 


.0520 


2 


.2210 


29 


.1360 


56 


.0465 


3 


.2130 


30 


.1285 


57 


.0430 


4 


.2090 


31 


.1200 


58 


.0420 


5 


.2055 


32 


.1160 


59 


.0410 


6 


.2040 


33 


.1130 


60 


.0400 


7 


.2010 


34 


.1110 


61 


.0390 


8 


.1990 


35 


.1100 


62 


.0380 


9 


.I960 


36 


.1065 


63 


.0370 


10 


.1935 


37 


.1040 


64 


.0360 


II 


.1910 


38 


.1015 


65 


.0350 


12 


.1890 


39 


.0995 


66 


.0330 


13 


.1850 


40 


.0980 


67 


.0320 


14 


.1820 


41 


.0960 


68 


.0310 


15 


.1800 


42 


.0935 


69 


.02925 


16 


.1770 


43 


.0890 


70 


.0280 


17 


.1730 


44 


.0860 


71 


.0260 


18 


.1695 


45 


.0820 


72 


.0250 


19 


.1660 


46 


.0810 


73 


.0240 


20 


.16/ 


47 


.0785 


74 


.0225 


21 


.1590 


48 


.0760 


75 


.0210 


22 


.1570 


49 


.0730 


76 


.0200 


23 


./540 


50 


.0700 


77 


.0160 


24 


./520 


51 


.0670 


76 


.0160 


25 


./495 


52 


.0635 


79 


.0145 


26 


./470 


53 


.0595 


80 


.0135 


27 


.1440 


54 


.0550 







Table No. 2. 



126 





spsbjqx 


it^XX"»i-*'-i'^'^'-'*O0XO0O000O0O0OC«O0O0X 


U 

a 

cu 

bo 

c 
o 

ll 
*J 
03 

(S 

X 

o 
n 

V 

■4-i 
Wi 

u 
a 
o 

u 


t^XX^Tl<rtrtrf^XXXXXXXXXXXX 


a 

a. 

c 
o 

u 

•4-1 

03 

CO 

u 

W 

fl 
o 

Q 

tM 
o 

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u 
4^ 

Ih 

u 

o 

u 






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. 1 ^ C: i~ i-~ X ^ X c; S: ;C — ' u- c^i -q — t^ — l- o 


Ci^^CiCit^OCCMt^i-'Jt^t^C^lTtixt^Ci-'I'-IO 

:m o t^ o ^; '— o o o CD c>4 ^ c: c-1 1-'; i-o -o o c^i c-1 o 

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re •* o ^^ cc L-; ^? i-o o c-i 

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r-i^fNCOTj^LOXC^ioC-IOXCC 

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X --TI1 re— . 

o — M Tf -^ ,- o -^ C5 X rt — ei ri -^ 


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ei ic Til ^ t^ M c: re o c m 

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c; ei X — o X t^ ei t^ X i-e — c; ue c 
i-e t^ o Le C2 -^ o i-e t^ r- — re X i-e re 


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IBnjajni 


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iiiiiiiiliiigiiigggiig 


re X C-- ^ "-- c: — r: i.- — C-. v; c. r~ ^: :D n ^ o c-1 
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oo^^cJ^i^eit^c^ci»-ex-T:e — ^ci^r^D'^o-r 


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^c,cc^t^o-.202xxogxg2 


t-i.-ici^oX'-i-'j'X'nTricx-^x 
■-I'-i'-iiMce^icr^c; 


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rrc;^'-eoc:^:oorecc:xi>-oi-eiOT}<re:e!M 


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iiiiSS=:32igS?lilsisliiSg 


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X Tf TJ1 X ^ ei X cq d X o Le i-e Le 

c; — oxOTfoo^x — uer^t^t^ 
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o c: ei rr re >-e t^ c: re — c; ue — X — i-e M M ci ue i-e 

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rt.-i--"M(NC«:cO-q"J<i---^t^I:^XC: — N 




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o m ue ue ue re ue ue ue ue 

o ^ t^ Tj> LI — -^ t^ t^ o M M n M i-e ue 

T^ujoxoreoc; rexLeoLeoi-e^ooot^ir^ 


lO in in re in in in 

rp un -H o o i> t^ o o ei e-1 c) 
xoreocirexinoinomcTwO 




»— 1 (—1 


—ir-i— irtc^(Mre'5'Tr<ininot^x 




azig 
[Bmnio^ 


12; 


-««-+»«»Hr<e*-rt T^-OCQ -t<N -o^ -wiij O t~ X O C --^ ?> 
1-1^ a CO tP _ _- _, 


--ftc-+^c*nHNK*-^^H -+?r*»c<j -e*re -w^ -e*in co t^ 00 O O (N 

^ rt M re ^ — — 


■*<nHit-H .-t-?.-fr«C^ HnrC ^♦^"'^ -Win O I> X 

^ — CI re T!< 



127 



Table No. 3. 




-^ 

V — P- 3tand.P/uj' Oept/, - ^Hu 
D-Diam. P/uq Small End (I t \ 
t~ r/t/cA oFTongue 

■ xy////////yy///y/////M 



No. 



1 

2 
3 
4 
5 
6 



9 
9 
10 
10 
11 
12 
13 
14 
15 
16 




1 
2 
3 
4 
5 
6 



-H-Oepfh ofHo/e 
-B~Len3fh of Shan A 




STANDARD TAPERS 



-S- Dept/i of S/jank 




mm. 

t M- 



M- Taper per foot 
of- DIam. of Tonyt/e 
Al- Taper per Inch 



-K- 




D 



B 



H 



K 



W 



R 



M 



.20 


.2390 


II 


li 


ItV 


H 


f 


.25 


.2994 


1t\ 


lA 


ifV 


IH 


i 


.312 


.3953 


2 


2rV 


2* 


IH 


# 


.35 


.4020 


li 


If 


If 


n^ 


-u- 


.45 


.5229 


U 


2/. 


u 


MJ- 


f 


.50 


.5989 


2^ 


2f|^ 


2i 


2^1 


i 


.60 


.7250 


3 


3f 


B,^ 


2|^ 


-H 


.75 


. 8984 


'^h 


4i 


3!^ 


B|f 


1 


.90 


1 . 0G(i7 


4 


4f 


4* 


B* 


H 


.90 


1.0770 


4i 


5 


4f 


4* 


H 


1.0446 


1.2596 


5 


6,V 


5i 


4|l 


h% 


1.0440 


1.2888 


^\\ 


6J 


■5!^ 


5,V'* 


1^ 


1.25 


1.5312 


6i 


7R 


C| 


«^l 


l/r, 


1.50 


1.7968 


T* 


8^,- 


7i 


^\% 


u 1 


1.75 


2.0729 


1\ 


8^-1 


7i 


1h 


1^ 1 


2. 


2.3438 


8i 


n 


8| 


^h. 


ni 


2.25 


2.6146 


8| 


10 


«* 


m 


Hh 


2.50 


2.8854 


^\ 


10^ 


9| 


9 


n 



.135 
.166 
.197 
.228 
.260 
.291 
.322 
.353 
.385 
.385 
.447 
.447 
.447 
.510 
.510 
.572 
.572 
.635 



A 



T5' 



if 



9 

T(f 

il 

Iff 

.■) 2 
f 



N 



.170 


7^ 


A 


.030 


lt¥ 


.500 


.220 


t'o- 


A 


.030 


u 


.500 


.282 


y\ 


iIt 


.040 


2f 


.500 


.320 


A 


.5 
16 


.050 


m 


.500 


.420 


i 


vV 


.060 


2A 


.500 


.460 


#T 


Tir 


.060 


2| 


.500 


.560 


T% 


# 


.070 


m- 


.500 


.710 


?.4- 


f 


.080 


H 


.500 


.860 


f 


t'« 


.100 


4f 


.500 


.860 


f 


T'iT 


.100 


4| 


.500 


1.010 


fv 


tV 


.110 


51-1 


.5161 


1.010 


iV 


tW 


.110 


6B 


.5161 


1.210 


Te 


i 


.130 


7iVI 


500 


1.460 


* 


i 


.150 


7|| 


.500 


1.710 


i 


^ 


.170 


8A 


.500 


1.960 


tIt 


f 


.190 


9A 


.500 


2.210 


yV 


* 


.210 


9|4 


.500 


2.450 


t 


1 


.230 


101 


.500 



.0416 

.0416 

.0416 

.0416 

.0416 

.0416 

.0416 

.0416 

.0416 

.0416 

.043 

.043 

.0416 

.0416 

.0416 

.0416 

.0416 

.0416 



.252 


.356 


2 


2H 


2.tV 


m 


-1^- 


.160 


i 


.24 


iff 


if-T 


.04 


2A 


.625 


.369 


.475 


2* 


2/ff 


2t^ 


2rV 


f 


.213 


t\ 


.35 


u 


fV 


.05 


2| 


.600 


.572 


. / 


2T"ff 


3tV 


2| 


n 


i 


.26 


t 


H 


i 


i 


.06 


21 


.602 


.778 


.938 


3r\ 


31 


H 


3tV 


IrV 


.322 


Vrr 


f 


y\ 


^T 


.08 


3A 


.602 


1.02 


1.231 


4rV 


4| 


U 


3^ 


li 


.478 


* 


H 


it 


A 


.10 


4^ 


.623 


1.475 


1.748 


5t=V 


6 


51 


4H- 


U 


.635 


f 


i« 


* 


f 


.12 


51 


.630 


2.116 


2.494 


n 


8^ 


n 


7 


If 


.76 


* 


2 


* 


^ 


.15 


8 


.626 


2.75 


3 27 


10 


11§ 


10^ 


9,V 


2f 


1.135 


If 


21 1 


H 


f 


.18 


111 


.625 



.05208 

.05 

.05016 

.05016 

.05191 

.0525 

.05216 

.05208 



Table No. 4. 



128 




G/iG£ L/NES — Rii^ET Spacing ; — 



I Beams Carnegie 


Depfh 


WeigM 


A 


Max. 
Riyet 


2A- 


80-/00 


4- 


V6 


zo 


80-100 


4 


f| 


20 


65-75 


j;i 


f/ 


18 


55-10 


J^ 


%t 


15 


80-100 


5h. 


II 


15 


60-75 


3^ 


3/4. 


15 


42-55 


3 


II 


/z 


40-55 


3 


u 


IZ 


3/^-35 


2^ 


It 


10 


15-40 


2^8 


u 


9 


ZI-35^ 


2yz 


II 


8 


I8-Z5k 


zy^ 


» 


7 


15-ZO 


zy4- 


Ve 


6 


IZk-l7A 


z 


II 


5 


d^-14^ 


I'A- 


Vz 


4- 


7J£-I0i 


lyz 


tt 


3 


5>^-7>^ 


1^6 


V8 




Channels Carnegie 


Dcpffi 


Weight 


A 


Max. 
Rivet 


15 


45-55 


zy^ 


i/^ 


75 


33-40 


iVs 


II 


12 


30-40 


z 


II 


IZ 


ZOk-25 


/^ 


II 


10 


25-35 


2 


II 


10 


15-20 


lyz 


» 


9 


20-25 


1^4- 


tl 


9 


15^4-15 


1% 


If 


5 


I6^-2IA 


lyz 


II 


8 


llMr/3^ 


ly^ 


II 


7 


l7^iSk 


lyz 


Ys 


7 


3h-m 


ly^- 


II 


6 


l3-/5Ji 


1% 


H 


6 


8-10/2 


lys 


II 


5 


d-llA 


ly^ 


'/z 


5 


syz 


I 


H 


4- 


5y4-7k 


1 


II 


3 


4-6 


% 


■Ve 




k M M — 1\ 



For 8' only 



Rivet Dimensions 

v4^ 



Angles Amer. Br.Co. 


Leg 


A 


B 


c 


Max. 
fiii/et 


8 


4^ 


5 


3 


Vs 


7 


4 


2i^ 


J 


II 


6 


S^z 


zy^ 


2>2 


It 


*6 


zyz 


2'/i 


z:/^ 


II 


5 


3 


2 


/^ 


tl 


4 


24 






II 


SVa 


2 






II 


3 


ly^ 






It 


m 


m 






3/4. 


Z'/z 


lya 






% 


zy^ 


ly^- 






// 


2 


1^8 






'/2 


\y^ 


1 






II 


lyz 


V8 






ys 


iy^f- 


^ 






II 


1 


^6 






'A 




* For thick, oyer ^ 




2.- Bars Amen Br Co. 


Norn. 
Web 


Thick. 


A 


B 


Max. Riv. 
A B 


6 


Vs-Vs 


zy^ 


3 


Vs 


Vs 


5 


%-M 


zys 


Z'^ 


•1 


II 


5 


^6-^ 


2 


r/z 


II 


II 


4 


%-% 


2 


z 


^ 


It 


4 


^^-^^ 


/^ 


2 


/' 


II 


4 


J^-^ 


/^ 


2 


II 


11 


3 


y/(ryz 


1% 


jyz 


If 


¥)■ 


3 


y^-% 


lyz 


lyz 


II 


II 



Minimum Clearances 




MiN. Rivet Spacing 



,,L ,,,1- ,f., 



^ 




T- Bars Cambria 


Flange: 


Stem 1 


Wdt 


A 


Max 


Dpth 


B 


Max 
/P/V. 


5 


zye 


^ 


4 


24 


/ 


4'/z 


1'4 


tt 


A 


2 


• 


4 


2 


% 


3 


/^ 


^5 


I'/z 


Ih 


' 


Z'/z 


/^ 


^ 


3 


lyz 


Vz 


24 


jy^ 


" 


Z\ 


lya 


•• 


Z 


/ye 


^8 


2^ 


jy^ 


u 


ih 


/ 


- 


Z'A 


lys 


It 


Ih 


y^ 


'/z 


2 


1 


" 


iy4. 


% 


H 


/^ 


n 


^ 


ly. 


ya 


1 


/^ 


" 




lye 


^. 


" 


M 


It 


tl 


iJfs 


H 


% 


ih 


» 


II 


1 


It 


- 


1 


1 . 


It 









TRIVET Dimensions 











. 


Clearance 















_ 


Clearance 


-. 











R/yc 1 i^/nrcr^oiu/va 


OPAC//VCI 


R/irc / L/z/yic^/vj/unf:) 




V 


^1 


D/am. 


D 


E 


F 


G 


H.= f< 


L 


7^ 


D/am. 


D 


£ 


F 


G 


H^K 


L 


7^ 




^^ 


i; 


^. 


ya 


"Ae 


4^/6 


V8 


y/6 


^8 


ly^ 


Va 


3/4. 


/y^ 


3y/6 


7^/6 


ya 


Va 


Z'A 


ly^ 


DU-£-> 


y^ 


y<5 


ya 


v^ 


'y^- 


'y^e. 


7% 


1 


Vs 


/^6 


ya 


/ya 


V/6 


7 


2^ 


/yz 


X 


Vs 


/;/. 


% 


1 


•T/e 


^V/s 


7Va 


/ya 


1 


7ya. 


'Vis 


/y/6 


ya 


/^^ 


3 


7:^3 






^ 



T 

F 

1 



129 



Table No. 5. 



Ball Crank Handles 



Machine Handles 



Standard Washers 



















a; /J M 


). of Mach.Hand/&. 


No. 


A 


B 


c 


D 


^ 


r 


G 


H 


J 


K 


L 


M 


1 


3^3 


l^z 


/4l 


% 


5§. 


^ 


^. 


yz 


^. 


y,e 


% 


/ 


Z 


dJi 


/^a 


/'/s 


/^^ 


^a-a 


^ 


%^ 


% 


%z 


% 


% 


/ 


J 


4- 


/^ 


J^e 


ly^ 


/^^ 


^ 


%a 


% 


%z 


^ 


ye 


2 


4- 


4i 


I'i. 


iZ 


/^e 


/^ 


Vs 


/9/ 


^ 


'A 


% 


^ 


2 


5 


5 


/^ 


2^^ 


/^ 


/^ 


y?6 


% 


% 


^ 


'/s 


'/z 


3 


6 


5^z 


2 


2^4. 


/^ 


/^. 


1 


%- 


ys 


yz 


% 


yz 


J 


7 


6 


2h 


2>. 


/^ 


/;! 


1 


h- 




yz 


"%. 


% 


3 


8 


6A 


Z^e 


2^4 


/;§ 


/^ 


/ 


%. 


IS/ 


yz 


I^s 


% 


4 


9 


7 


2^a 


5 


/^ 


//. 


/ 


'A. 


■^e 


'/e 


l^e 


% 


^ 


10 


7l 


Z^s 


j4 


/;! 


/^ 


1 


h- 


^6 


% 


/ya 


'^s 


5 


II 


8 


3'/8 


J#^ 


/# 


/^ 


/4 


%. 


% 


'A 


/^ 


^s 


5 


12 


8'/a 


Jl 


5% 


/^ 


/#. 


/^ 


h 


/ 


% 


/^ 


% 


6 


IS 


9 


J^ 


d% 


/4^ 


/^ 


/^ 


^ 


/^. 


^ 


/M 


X 


6 



No. 


A 


B 


c 


D 


£ 


F 


G 


H 


J 


/? 




1 


2^4- 


yz 


^z 


'^6 


%z 


yz 


^e 


yz 


^ 


y^ 




2 


zy^ 


% 


ya 


"/e 


%z 


% 


ya 


^/e 


^e 


^6 




J 


3y6 


%- 


ys 


I 


yz 


% 


ya 


ya 


ya 


¥8 




4 


S^z 


^ 


r3z 


1^6 


'y3z 


'A 


ye 


% 


y/6 


^^2 




5 


4- 


ye 


^6 


l/s 


y,6 


'y3z 


y/e 


^ 


yz 


ye 




6 


4-% 


V8 


yjz 


/^. 


%z 


^6 


'rs^ 


'#. 


% 


V/e 





Ball Lej^er Handles 




\^P -^A dots not 
aff)/y fo this. 



No. 


A 


B 


c 


D 


E 


r 


G 


H 


N 





p 


1 


41 


3k 


lye 


Va 


ya 


ye 


y^. 


ya 


ys 


yz 


1 


2 


syz 


4-^6 


/^ 


/ 


'y/6 


yz 


% 


ya 


ya 


yz 


/ya 


J 


6!^z 


S 


Jh 


/ 


^ 


% 


/ 


ye 


ya 


yz 


ly^ 


4 


lyz 


6 


/^ 


/ 


'A 


9^e 


/ 


% 


ye 


ya 


jye 


.5" 


ayz 


eys 


jh 


jya 


^ 


ya 


/4 


'y,6 


ye 


H 


lys 


6 


9 


7^^ 


/h 


/>^6 


% 


ya 


/js 


% 


y/e 


% 


/^ 



% 

i 


1 


1 

1 




r 


3/6 


>4 


% 


/#^ 


2>700 


y^ 


ye 


^ 


16 ye 


1330 


ye 


ya 


ye 


16 ye 


IIZO 


ya 


ye 


1 


14 M^ 


680 


ye 


yz 


/A 


14^4 


430 


y^ 


% 


/ya 


iz y^* 


Z70 


% 


ya 


/ya 


12 '44 


Z30 


% 


% 


1% 


10 ^ 


/30 


^4. 


% 


z 


/o^^ 


/GO 


ya 


% 


2X 


9 S 


75 


1 


/Jfe 


Z'^ 


9 ^ 


62 


/ya 


/M 


z% 


9 ^3Z 


5Z 


lA 


/ya 


5 


9 Mz 


4-0 


lys 


/yz 


3^4. 


8 ^ 


5Z 


lya 


/ye 


3yz 


6 1* 


28 


lya 


/M3^ 


8 ^ 


Z4 


iMiya 


4 


8 Z 


ZZ 


/ya 


z 


4i 


8 Z 


/9 


z 


zya 


4^ 


8 ^ 


/? 


za 


Z%4% 


6 ^ 


/J 


zyz 


zye 


5 


5 ^ 


// 



Table No. 6. 



130 



i 
i 
I 







o. 



«o 



*^ 



ini 





S 
IC 


Ji! 


Y\ 


1^ 


^ 




a^ 


'Xi 


Hv 




<0 




N 
^ ^ 


.^ 


1 


c3 




II 

k 


K^ 



^ 



(0 



o. 



-J 



^ 



C5 



k 



kj 



Q 









-to 






SM 






~|0O 



-l^J- 



•^liS 



<nii5 






S<M 



H^ 



<ntS 



-IM 



-In 



C\J 



!5|vo 



t*)10D 



^ 



H<M 






•filoo 



■oloQ 






Noo 



'*>l'10 



^l:* 



N«<j 



'Olio 



-IM 






.^iS 



H^ 



-IM 



W^ 



U^IoqIoIso 



-loo 



•ol!* 



l^l«0 






-1^ 



Ni» 



rol-i- 






^O 



'^lip 



H^^ 



-IM 



^ 



Noo 
HcvJ 

-loo 



KOjOO 



^vo 






i^loo 



:iio 



Noo 



•^loo 









li5 



lOloo 



Noo 
Hoo 



Hvo 



:|!« 



Moo 



N^ 



:|vo 



M<o 



Nrj 






^^ 









i»)loo 



"olaj \tifia 



toloo 



Moo 

Hi 



NiS 



Hm 



>|M 



N<c 






cnliP 



•loa 



■^loo 



i^loo ■ 



rol'sj- 



•IM 



Moo 



N|Oo 



■^100 









Noo 



N|0O 






l^lOO 

Hoo 



-loo 



MM 



■^loo 



Mao 

^i 



MOO 

-1^ 



00 



00 



00 



Moo 



-|«o 
Mm 

:^ 



M^ 



-1^ 
-1^ 



00 

■^ico 

-1^ 



CO 

-loo 
i*)|oo 






-|(\( 

■^loo 
i^Ioo 



M55 



NliO 






SM 



'IM 



-IM 



<n|5S 



<nl50 



•^Ico 



^i5 



i^^l- 



5JV0 



!r>i^ 



Nloo 



•^It 



•ol^t 



"^14! 



•1-^ 



51 vo 



-»,lvO 



Nloo 



^1^ 



5215$ 



-1^ 



'JOQ 



^^liO 



-1^ 



k>|V8 



"itOQ 



M^o 






-l^j. 



00 



0^ 



^§ 



Si 



■^lao 



SSi 






i^ 



•~|00 
5© 



-^ 



c?> 



'Oloo 



Hi 



Soo 



-I'M 



Moo 



M^ 






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Hemlock 

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132 



133 



INDEX 



Addendum, tooth . 
Alterations, blue prints 

" lettering 

Anchor bolts 
Angle gears 
Angles, specif jing 
" structural 
Architectural lettering 
Arrows 
Artists' perspective 

A. S. M. E. Stand, screws 
Assembly Drawings 
Asometric 

" cube 

" exercises 

Ball handles 

B. & S. tapers 
Batten plate 
Belting 
Bend . 
Bevel gears . 
Bevels, structural . 
Bill of material 
Birm. -wire gage 
Black printing 
Blue printing 
Blueprints, alterations 
Bolts, general 

" manuf. stand. 

" U. S. stand. 
Bond paper . 
Broken ends 
Building plan 



Cabinet projection 
Castings 



exercises 



SECTION 

134 
89 
317 
108 
149 
57,68 
169, 175, Tab. 5 
296, 301 
47 
6, 211, 270 
117, Tab. 2 
21 
10, 230-257 
233 
258 

Tab. 6 

132, Tab. 4 

175 

78 

130 

142 

159 

84 

133 

90 

86 

89 

107 

111 

110, 111, Tab. 1 
86 
26 
176 

8, 264-266, 274 

267 

41 



Center lines . 
Chain . 
Channel 

Checking drawings 
Chord . 
Circular mil , 
Circular pitch 
Clearance, rivet 

tooth . 
Clevis 
Clip angle 
Coach screw 
Coping, structural 
Cotter 

" pin . 
Coupling, pipe 
shaft 
Cover plate 
Crimped angle, struct. 
Cross, hatching 
Cross, pipe 
Cross, section paper 
Cj'cloidal teeth 

Decimal equivalents 

Dedendum, tooth . 

Detail drawing 

Diametral pitch 

Dimensioning 

Dimension figures . 
" lines 

" location 

" selection 

Dotted lines 

Drilled holes 

Elbow, pipe . 
Electrical svmbols 



165. 



44 



SECTION 

36 

78 

169, 175 

207 

175 

78 

. 134-137 
174, Tab. 5 
134, 137 
175 
175 
119 
175 
126, 127 
175 
130 
Tab. 7 
175 
175 
33,35 
130 
202 
138 

Tab. 1 

134, 137 

21 

135 

37-72. 173 
58-64 

46, 53. 173 
72 
38 
29 
78 

130 
209 



134 

Elevation 
Ellipse, isometric 
" sketching 
Exercises 
Extension lines 
Eye bar 

Face of tooth 
Field rivets . 
Filler, structural 
Fillets on castings 
Fillet, tooth . 
Finish marks 
Flange coupling 
Flange, structural 
Flank of tooth 
Flats . 
Forging 
Foundry plan 

Gage, machine screw 

" steel wire 

" twist drill 

" U. S. sheet metal 

" wood screw . 
Gage lines 
Gages 

Gear books . 
Gearing, toothed . 
Gear teeth 
Gib head key 
Gusset plates 

Hanger, shaft 
Hatching, cross 
Helix angle . 
Hitch angle, struct. 
Horizon Une 
Horizontal projection 

I beam 
Involute teeth 



SECTION 

18 
260 
200 
208, 224, 258, 263, 267 

48 
175 

134 

175 

171, 175 

41 
134 

41 

Tab. 7 

175 

134 

175 

39 
176 

Tab. 2 

133, Tab. 2 

Tab. 2 

78, 133 

Tab. 2 

164, 175, Tab. 5 

133 

150 

134-150 

134-139 

. 122 

170, 175 

78 

33 

. 146 

175 

219 

18 

169, 175 
138 



Isometric drawing 
" exercises 
" paper 
" projection 

Jarno taper . 

Keys 
Key sizes 

" Whitney or Woodruff 
Knurled head 

Lacing 
Lag screw 
Lateral pin . 
Lattice bars . 
Laying out floor 
Lead of a screw thread 
Lengths, estimating 
Lettering 

Alphabets 

Alterations 

Books on 

Mechanical 

Photo reproduction 

Practice work 

Principles 

Titles . 
Linear perspective 
Line shading 
Lines of a drawing 

Center lines 

Dimension lines 

Dotted lines . 

Extension lines 

Shade lines 
Lug angle 

Machine handles 

" screws 
Map titles 
Materials, weight of 



SECTION 

12, 259-262, 272 
263 
262 
11 

132 

122 

123 

124, Tab. 1 

112 

175 
119 

175 
172, 175 
152 
104 
180 
284 
296-297 
317 
318 
285 
315, 316 
303-314 
288-295 
298-302 
5, 210, 218, 269 
277-283 
80-81 
36,81 
44, 81,173 
29,81 
48,81 
275, 276 
175 



78, 



Tab. 6 
L17, Tab. 2 
300 
Tab. 8 



Mitre gears 
Model drawing 
Morse tapers 

Nominal sizes 

Normal pitch 

Notes appended to drawings 

Nuts, standard 

ObHque projection 
Old English 
Open holes, struct. 
Orthographic projection 
Outlet, pipe fitting 

Panel, struct. 
" point 

Perspective, Artists' 
" linear 

" principles 

Picture Plane 

Pillow block 

Pin plate 

Pipe, standard 

Pipe fittings 

Pitch Une of gears 

Pitch of gear teeth 

Pitch of rivets 

Pitch of roof 

Pitch of thread 

Plan view 

Plotting curves 

Plug, pipe fitting . 

Positive prints 

Projection, cabinet 
" horizontal 

" isometric 

" obUque 

" orthographic 

" profile 

" sketches 

" third angle 



110 



SECTION 

149 

223-229 
132, Tab. 4 

78 
145 

74 
111, Tab. 1 

7,273 

297 

161, 175 

9 

130 

175 
175 

6, 211, 270 

5, 210, 269 

. 212-222 

5 

78 

175 

78, 129, Tab. 3 

130 

134 

134-137, 145 

. 167, 175 

175 

103 

18 

. 201, 241 

130 

90 

8, 264-266, 274 

18 

11 

7, 273 

9, 271 

18 

202-206, 208 

15 



Projection, vertical 

Pulleys 

Purhn, struct. 

Rack 

Reducing coupling 

Riser, pipe 

Rivets . 

Rivet clearances 

" dimensions 

" signs 

" spacing 
Rolled sections 
Rope 

Rounded corners 
Run, pipe fitting 

Scales for a drawing 
Screw gage . 
Screws, cap 

coach 

drawing of 

fillister head 

flat head . 

machine 

round head 

set . 

wood 
Screw threads. Acme 

buttress . 

conventional 

double 

International 

knuckle . 

left hand 

multiple . 

pipe 

single 

sketching 

square 

U. S. standard 



78, 



135 

SECTION 
18 

41, 78 
175 

141 
130 
131 
121 

Tab. 5 

Tab. 5 

162 

Tab. 5 

169 

78 

41 

130 

22. 23, 155 
Tab. 2 
113-116 
119 
102-105 
112 
112 
117, Tab. 2 
112 
112, 116 
78, 120 
99 
96, 97 
102 
104 
94 
100 
105 
104 
101 
103 
244 
98 
93 



136 



Screw threads, Vee 

Whitworth 

Secondary members 

Section lining 

Section symbols 

Sections 

Separator 

Shade lines . 

Shafting, size of 

Sheared plate 

Sheaves 

Sheet metal gage 

Shop rivets . 

Sketching of angles 
" axometric 
" of circles 
" of cube 
" of ellipses 
" exercises 
" of hexagons 
" Isometric 
" Projection 
" of threads 
" of triangles 

Sole plate 

Specifications on drawing! 

Spiral gears . 

Splice plate 

Spring cotter 

Springs 

Sprockets 

Spur gears 

Stay plate 

Straight coupling 

Structural drawing 

Stubs' Iron Wire gage 

Stud bolt 

Sub titles 

Tap bolt 
Tapers 



SECTION 

92 

95 

175 

33,35 

34 

30 

175 

275, 276 

78, Tab. 7 

175 

78 

78, 133 

175 

181 

230-257 

191 

226 

200 

208, 224, 258, 263, 267 

189 

262 

202 

24 4 

187 

175 

73-77 

144 

175 

127 

128 

78 

140 

175 

130 

151-175 

133 

107 

73 

107 
78, 132, Tab. 4 



Tapped holes 

T bar . 

Tee, pipe fitting 

Templets 

Third angle projection 

Through bolt 

Tie plate 

Titles . 

Tooth angle 

Tooth proportions . 

Tracing cloth 

Truss . . ■ . 

Tubing 

Twist drill gage 

Union, pipe . 

Universal mill plate 

Upset rods 

U. S. standard bolts 

U. S. standard gage for plate 



Vanishing points . 
Velocity ratio 
Vertical projection 
Views, selection of 

Wall brackets 
Washers 
Web plate 
Weight of materials 
Whitney keys 
Wire gage 
Wood screws 
Working drawings 
Working lines 
Worm gearing 
Wrought iron pipe 

Y branch, pipe fitting 

Zbar . 



SECTION 

106 

169, 175 

130 

152 

15 

107 

175 

298-302 

146 

137 

86 

175 

78 

133, Tab. 2 

130 
175 
175 
110, 111, Tab. 1 
133 

218 

149 

18 

24 

78 
118, Tab. 6 
. 171 ,175 
Tab. 8 
124, Tab. 1 
133 
78, 120 
19-85, 151-173, 207 
. 158, 175 
143 
129, Tab. 3 

130 

. 169, 175 



/COPY. DEI TO CAT. DIV, 

NOV 9 1509 



LIBRARY OF CONGRESS 



019 936 895 



